Abstract

Using a similarity transformation, we obtain analytical solutions to a class of nonlinear Schrödinger (NLS) equations with variable coefficients in inhomogeneous Kerr media, which are related to the optical rogue waves of the standard NLS equation. We discuss the dynamics of such optical rogue waves via nonlinearity management, i.e., by selecting the appropriate nonlinearity coefficients and integration constants, and presenting the solutions. In addition, we investigate higher-order rogue waves by suitably adjusting the nonlinearity coefficient and the rogue wave parameters, which could help in realizing complex but controllable optical rogue waves in properly engineered fibers and other photonic materials.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. N. Akhmediev and E. Pelinovsky, “Introductory remarks on “Discussion & Debate: Rogue Waves – Towards a Unifying Concept?” Eur. Phys. J. 185(1), 1–4 (2010).
  2. K. B. Dysthe and K. Trulsen, “Note on breather type solutions of the NLS as a model for freak-waves,” Phys. Scr. T 82(1), 48–52 (1999).
    [Crossref]
  3. V. V. Voronovich, V. I. Shrira, and G. Thomas, “Can bottom friction suppress ‘freak wave’ formation?” J. Fluid Mech. 604(2), 263–296 (2008).
  4. D. Clamond, M. Francius, J. Grue, and C. Kharif, “Long time interaction of envelope solitons and freak wave formations,” Eur. J. Mech. BFluids 25(5), 536–553 (2006).
    [Crossref]
  5. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
    [Crossref] [PubMed]
  6. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Rogue waves and rational solutions of the nonlinear Schrödinger equation,” Phys. Rev. E 80(2), 026601 (2009).
    [Crossref] [PubMed]
  7. W. P. Zhong, M. R. Belić, and T. Huang, “Rogue wave solutions to the generalized nonlinear Schrödinger equation with variable coefficients,” Phys. Rev. E 87(6), 065201 (2013).
    [Crossref] [PubMed]
  8. W. P. Zhong, M. Belić, B. A. Malomed, and T. Huang, “Breather management in the derivative nonlinear Schrödinger equation with variable coefficients,” Ann. Phys. 355(2), 313–321 (2015).
    [Crossref]
  9. A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Rogue waves and rational solutions of the Hirota equation,” Phys. Rev. E 81(4), 046602 (2010).
    [Crossref] [PubMed]
  10. S. Chen and L. Song, “Rogue waves in coupled Hirota systems,” Phys. Rev. E 87(3), 032910 (2013).
    [Crossref]
  11. Y. Ohta and J. Yang, “Rogue waves in the Davey-Stewartson I equation,” Phys. Rev. E 86(3), 036604 (2012).
    [Crossref] [PubMed]
  12. D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6(7), 463–468 (2012).
    [Crossref]
  13. G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber super continuum generation in the picosecond regime,” Appl. Phys. B 94(2), 187–194 (2009).
    [Crossref]
  14. J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nat. Photonics 8(10), 755–764 (2014).
    [Crossref]
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    [Crossref]
  16. E. A. Kuznetsov, “Solitons in a parametrically unstable plasma,” Sov. Phys. Dokl. 22, 507–508 (1977).
  17. Y. C. Ma, “The perturbed plane-wave solutions of the cubic Schrödinger equation,” Stud. Appl. Math. 60(1), 43–58 (1979).
    [Crossref]
  18. D. H. Peregrine, “Water waves, nonlinear Schrödinger equations and their solutions,” Soc. Ser. B: Appl. Math. 25(1), 16–43 (1983).
  19. N. Akhmediev, V. Eleonskii, and N. Kulagin, “Exact first-order solutions of the nonlinear Schrödinger equation,” Theor. Math. Phys. 72(2), 809–818 (1987).
    [Crossref]
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    [Crossref]
  21. S. Chen, F. Baronio, J. M. Soto-Crespo, P. Grelu, and D. Mihalache, “Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems,” J. Phys. A Math. Theor. 50(46), 463001 (2017).
    [Crossref]
  22. M. Onorato, S. Resitori, and F. Baronio, eds., Rogue and Shock Waves in Nonlinear Dispersive Media (Springer, 2016).
  23. J. He, S. Xu, and K. Porsezian, “N-order bright and dark rogue waves in a resonant erbium-doped fiber system,” Phys. Rev. E 86(6), 066603 (2012).
    [Crossref] [PubMed]
  24. S. Chen, J. M. Soto-Crespo, and P. Grelu, “Dark three-sister rogue waves in normally dispersive optical fibers with random birefringence,” Opt. Express 22(22), 27632–27642 (2014).
    [Crossref] [PubMed]
  25. J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Express 17(24), 21497–21508 (2009).
    [Crossref] [PubMed]
  26. B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fiber optics,” Nat. Phys. 6(10), 790–795 (2010).
    [Crossref]
  27. K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
    [Crossref] [PubMed]
  28. B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, “Observation of Kuznetsov-Ma soliton dynamics in optical fibre,” Sci. Rep. 2(1), 463 (2012).
    [Crossref] [PubMed]
  29. A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, “Rogue wave observation in a water wave tank,” Phys. Rev. Lett. 106(20), 204502 (2011).
    [Crossref] [PubMed]
  30. A. Toffoli, D. Proment, H. Salman, J. Monbaliu, F. Frascoli, M. Dafilis, E. Stramignoni, R. Forza, M. Manfrin, and M. Onorato, “Wind generated rogue waves in an annular wave flume,” Phys. Rev. Lett. 118(14), 144503 (2017).
    [Crossref] [PubMed]
  31. W. P. Zhong, L. Chen, M. Belić, and N. Petrović, “Controllable parabolic-cylinder optical rogue wave,” Phys. Rev. E 90(4), 043201 (2014).
    [Crossref] [PubMed]
  32. W. P. Zhong, M. Belić, and T. Huang, “Solitary waves in the nonlinear Schrödinger equation with spatially modulated Bessel nonlinearity,” J. Opt. Soc. Am. B 30(5), 1276–1283 (2013).
    [Crossref]
  33. Z. Yan, “Nonautonomous ‘rogons’ in the inhomogeneous nonlinear Schrödinger equation with variable coefficients,” Phys. Lett. 374(4), 672–679 (2010).
    [Crossref]
  34. W. P. Zhong, “Rogue wave solutions of the generalized one-dimensional Gross-Pitaevskii equation,” J. Nonlinear Opt. Phys. Mater. 21(02), 1250026 (2012).
    [Crossref]
  35. W. P. Zhong and M. Belić, “Two-component vector solitons in defocusing Kerr-type media with spatially modulated nonlinearity,” Ann. Phys. 351, 787–796 (2014).
    [Crossref]
  36. W. P. Zhong, M. R. Belić, Y. Lu, and T. Huang, “Traveling and solitary wave solutions to the one-dimensional Gross-Pitaevskii equation,” Phys. Rev. E 81(1), 016605 (2010).
    [Crossref] [PubMed]
  37. J. R. He and H. M. Li, “Analytical solitary-wave solutions of the generalized nonautonomous cubic-quintic nonlinear Schrödinger equation with different external potentials,” Phys. Rev. E 83(6), 066607 (2011).
    [Crossref] [PubMed]
  38. X. Zhang, L. Wen, X. Luo, and Z. Xie, “Exact solutions of the generalized nonlinear Schrödinger equation with time- and space-modulated coefficients,” Phys. Lett. A 376(11), 465–468 (2012).
    [Crossref]
  39. D. Liang, Z. Yang, C. Liu, and W. Yang, “Optical rogue wave excitation and modulation on a bright soliton background,” Chin. Phys. Lett. 33(1), 010501 (2016).
    [Crossref]
  40. J. Zhou, H. Li, and J. He, “Analytical periodic wave and soliton solutions of the generalized nonautonomous nonlinear Schrödinger equation in harmonic and optical lattice potentials,” Commum. Theor. Phys. 58(3), 393–397 (2012).
    [Crossref]
  41. Z. Yan and C. Dai, “Optical rogue waves in the generalized inhomogeneous higher-order nonlinear Schrödinger equation with modulating coefficients,” J. Opt. 15(6), 064012 (2013).
    [Crossref]
  42. M. Belić, W. P. Zhong, and Y. Zhang, “Predictable rogue waves,” J. Opt. 18, 063001 (2016).
  43. L. Ling and L. C. Zhao, “Simple determinant representation for rogue waves of the nonlinear Schrödinger equation,” Phys. Rev. E 88(4), 043201 (2013).
    [Crossref] [PubMed]
  44. D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Classifying the hierarchy of nonlinear-Schrödinger-equation rogue-wave solutions,” Phys. Rev. E 88(1), 013207 (2013).
    [Crossref] [PubMed]
  45. W. P. Zhong, M. Belić, R. H. Xie, G. Chen, and L. Yi, “Two-dimensional Whittaker solitons in nonlocal nonlinear media,” Phys. Rev. A 78(1), 013826 (2008).
    [Crossref]
  46. N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, “Rogue wave early warning through spectral measurements,” Phys. Lett. A 375(3), 541–544 (2011).
    [Crossref]
  47. P. Gaillard, “Deformations of third-order Peregrine breather solutions of the nonlinear Schrödinger equation with four parameters,” Phys. Rev. E 88(4), 042903 (2013).
    [Crossref] [PubMed]

2017 (2)

S. Chen, F. Baronio, J. M. Soto-Crespo, P. Grelu, and D. Mihalache, “Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems,” J. Phys. A Math. Theor. 50(46), 463001 (2017).
[Crossref]

A. Toffoli, D. Proment, H. Salman, J. Monbaliu, F. Frascoli, M. Dafilis, E. Stramignoni, R. Forza, M. Manfrin, and M. Onorato, “Wind generated rogue waves in an annular wave flume,” Phys. Rev. Lett. 118(14), 144503 (2017).
[Crossref] [PubMed]

2016 (3)

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

D. Liang, Z. Yang, C. Liu, and W. Yang, “Optical rogue wave excitation and modulation on a bright soliton background,” Chin. Phys. Lett. 33(1), 010501 (2016).
[Crossref]

M. Belić, W. P. Zhong, and Y. Zhang, “Predictable rogue waves,” J. Opt. 18, 063001 (2016).

2015 (1)

W. P. Zhong, M. Belić, B. A. Malomed, and T. Huang, “Breather management in the derivative nonlinear Schrödinger equation with variable coefficients,” Ann. Phys. 355(2), 313–321 (2015).
[Crossref]

2014 (4)

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nat. Photonics 8(10), 755–764 (2014).
[Crossref]

W. P. Zhong and M. Belić, “Two-component vector solitons in defocusing Kerr-type media with spatially modulated nonlinearity,” Ann. Phys. 351, 787–796 (2014).
[Crossref]

W. P. Zhong, L. Chen, M. Belić, and N. Petrović, “Controllable parabolic-cylinder optical rogue wave,” Phys. Rev. E 90(4), 043201 (2014).
[Crossref] [PubMed]

S. Chen, J. M. Soto-Crespo, and P. Grelu, “Dark three-sister rogue waves in normally dispersive optical fibers with random birefringence,” Opt. Express 22(22), 27632–27642 (2014).
[Crossref] [PubMed]

2013 (7)

W. P. Zhong, M. Belić, and T. Huang, “Solitary waves in the nonlinear Schrödinger equation with spatially modulated Bessel nonlinearity,” J. Opt. Soc. Am. B 30(5), 1276–1283 (2013).
[Crossref]

Z. Yan and C. Dai, “Optical rogue waves in the generalized inhomogeneous higher-order nonlinear Schrödinger equation with modulating coefficients,” J. Opt. 15(6), 064012 (2013).
[Crossref]

P. Gaillard, “Deformations of third-order Peregrine breather solutions of the nonlinear Schrödinger equation with four parameters,” Phys. Rev. E 88(4), 042903 (2013).
[Crossref] [PubMed]

L. Ling and L. C. Zhao, “Simple determinant representation for rogue waves of the nonlinear Schrödinger equation,” Phys. Rev. E 88(4), 043201 (2013).
[Crossref] [PubMed]

D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Classifying the hierarchy of nonlinear-Schrödinger-equation rogue-wave solutions,” Phys. Rev. E 88(1), 013207 (2013).
[Crossref] [PubMed]

W. P. Zhong, M. R. Belić, and T. Huang, “Rogue wave solutions to the generalized nonlinear Schrödinger equation with variable coefficients,” Phys. Rev. E 87(6), 065201 (2013).
[Crossref] [PubMed]

S. Chen and L. Song, “Rogue waves in coupled Hirota systems,” Phys. Rev. E 87(3), 032910 (2013).
[Crossref]

2012 (7)

Y. Ohta and J. Yang, “Rogue waves in the Davey-Stewartson I equation,” Phys. Rev. E 86(3), 036604 (2012).
[Crossref] [PubMed]

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6(7), 463–468 (2012).
[Crossref]

J. Zhou, H. Li, and J. He, “Analytical periodic wave and soliton solutions of the generalized nonautonomous nonlinear Schrödinger equation in harmonic and optical lattice potentials,” Commum. Theor. Phys. 58(3), 393–397 (2012).
[Crossref]

X. Zhang, L. Wen, X. Luo, and Z. Xie, “Exact solutions of the generalized nonlinear Schrödinger equation with time- and space-modulated coefficients,” Phys. Lett. A 376(11), 465–468 (2012).
[Crossref]

W. P. Zhong, “Rogue wave solutions of the generalized one-dimensional Gross-Pitaevskii equation,” J. Nonlinear Opt. Phys. Mater. 21(02), 1250026 (2012).
[Crossref]

J. He, S. Xu, and K. Porsezian, “N-order bright and dark rogue waves in a resonant erbium-doped fiber system,” Phys. Rev. E 86(6), 066603 (2012).
[Crossref] [PubMed]

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, “Observation of Kuznetsov-Ma soliton dynamics in optical fibre,” Sci. Rep. 2(1), 463 (2012).
[Crossref] [PubMed]

2011 (4)

A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, “Rogue wave observation in a water wave tank,” Phys. Rev. Lett. 106(20), 204502 (2011).
[Crossref] [PubMed]

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, “Rogue wave early warning through spectral measurements,” Phys. Lett. A 375(3), 541–544 (2011).
[Crossref]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
[Crossref] [PubMed]

J. R. He and H. M. Li, “Analytical solitary-wave solutions of the generalized nonautonomous cubic-quintic nonlinear Schrödinger equation with different external potentials,” Phys. Rev. E 83(6), 066607 (2011).
[Crossref] [PubMed]

2010 (5)

Z. Yan, “Nonautonomous ‘rogons’ in the inhomogeneous nonlinear Schrödinger equation with variable coefficients,” Phys. Lett. 374(4), 672–679 (2010).
[Crossref]

W. P. Zhong, M. R. Belić, Y. Lu, and T. Huang, “Traveling and solitary wave solutions to the one-dimensional Gross-Pitaevskii equation,” Phys. Rev. E 81(1), 016605 (2010).
[Crossref] [PubMed]

A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Rogue waves and rational solutions of the Hirota equation,” Phys. Rev. E 81(4), 046602 (2010).
[Crossref] [PubMed]

N. Akhmediev and E. Pelinovsky, “Introductory remarks on “Discussion & Debate: Rogue Waves – Towards a Unifying Concept?” Eur. Phys. J. 185(1), 1–4 (2010).

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fiber optics,” Nat. Phys. 6(10), 790–795 (2010).
[Crossref]

2009 (3)

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Express 17(24), 21497–21508 (2009).
[Crossref] [PubMed]

N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Rogue waves and rational solutions of the nonlinear Schrödinger equation,” Phys. Rev. E 80(2), 026601 (2009).
[Crossref] [PubMed]

G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber super continuum generation in the picosecond regime,” Appl. Phys. B 94(2), 187–194 (2009).
[Crossref]

2008 (2)

V. V. Voronovich, V. I. Shrira, and G. Thomas, “Can bottom friction suppress ‘freak wave’ formation?” J. Fluid Mech. 604(2), 263–296 (2008).

W. P. Zhong, M. Belić, R. H. Xie, G. Chen, and L. Yi, “Two-dimensional Whittaker solitons in nonlocal nonlinear media,” Phys. Rev. A 78(1), 013826 (2008).
[Crossref]

2007 (1)

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
[Crossref] [PubMed]

2006 (1)

D. Clamond, M. Francius, J. Grue, and C. Kharif, “Long time interaction of envelope solitons and freak wave formations,” Eur. J. Mech. BFluids 25(5), 536–553 (2006).
[Crossref]

1999 (1)

K. B. Dysthe and K. Trulsen, “Note on breather type solutions of the NLS as a model for freak-waves,” Phys. Scr. T 82(1), 48–52 (1999).
[Crossref]

1987 (1)

N. Akhmediev, V. Eleonskii, and N. Kulagin, “Exact first-order solutions of the nonlinear Schrödinger equation,” Theor. Math. Phys. 72(2), 809–818 (1987).
[Crossref]

1986 (1)

N. N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrödinger equation,” Theor. Math. Phys. 69(2), 1089–1093 (1986).
[Crossref]

1983 (1)

D. H. Peregrine, “Water waves, nonlinear Schrödinger equations and their solutions,” Soc. Ser. B: Appl. Math. 25(1), 16–43 (1983).

1979 (1)

Y. C. Ma, “The perturbed plane-wave solutions of the cubic Schrödinger equation,” Stud. Appl. Math. 60(1), 43–58 (1979).
[Crossref]

1977 (1)

E. A. Kuznetsov, “Solitons in a parametrically unstable plasma,” Sov. Phys. Dokl. 22, 507–508 (1977).

Akhmediev, N.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Classifying the hierarchy of nonlinear-Schrödinger-equation rogue-wave solutions,” Phys. Rev. E 88(1), 013207 (2013).
[Crossref] [PubMed]

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, “Observation of Kuznetsov-Ma soliton dynamics in optical fibre,” Sci. Rep. 2(1), 463 (2012).
[Crossref] [PubMed]

A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, “Rogue wave observation in a water wave tank,” Phys. Rev. Lett. 106(20), 204502 (2011).
[Crossref] [PubMed]

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, “Rogue wave early warning through spectral measurements,” Phys. Lett. A 375(3), 541–544 (2011).
[Crossref]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
[Crossref] [PubMed]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fiber optics,” Nat. Phys. 6(10), 790–795 (2010).
[Crossref]

N. Akhmediev and E. Pelinovsky, “Introductory remarks on “Discussion & Debate: Rogue Waves – Towards a Unifying Concept?” Eur. Phys. J. 185(1), 1–4 (2010).

A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Rogue waves and rational solutions of the Hirota equation,” Phys. Rev. E 81(4), 046602 (2010).
[Crossref] [PubMed]

N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Rogue waves and rational solutions of the nonlinear Schrödinger equation,” Phys. Rev. E 80(2), 026601 (2009).
[Crossref] [PubMed]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Express 17(24), 21497–21508 (2009).
[Crossref] [PubMed]

N. Akhmediev, V. Eleonskii, and N. Kulagin, “Exact first-order solutions of the nonlinear Schrödinger equation,” Theor. Math. Phys. 72(2), 809–818 (1987).
[Crossref]

Akhmediev, N. N.

N. N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrödinger equation,” Theor. Math. Phys. 69(2), 1089–1093 (1986).
[Crossref]

Amiraranashvili, S.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Ankiewicz, A.

D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Classifying the hierarchy of nonlinear-Schrödinger-equation rogue-wave solutions,” Phys. Rev. E 88(1), 013207 (2013).
[Crossref] [PubMed]

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, “Rogue wave early warning through spectral measurements,” Phys. Lett. A 375(3), 541–544 (2011).
[Crossref]

A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Rogue waves and rational solutions of the Hirota equation,” Phys. Rev. E 81(4), 046602 (2010).
[Crossref] [PubMed]

N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Rogue waves and rational solutions of the nonlinear Schrödinger equation,” Phys. Rev. E 80(2), 026601 (2009).
[Crossref] [PubMed]

Arecchi, F. T.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Baronio, F.

S. Chen, F. Baronio, J. M. Soto-Crespo, P. Grelu, and D. Mihalache, “Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems,” J. Phys. A Math. Theor. 50(46), 463001 (2017).
[Crossref]

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Belic, M.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

M. Belić, W. P. Zhong, and Y. Zhang, “Predictable rogue waves,” J. Opt. 18, 063001 (2016).

W. P. Zhong, M. Belić, B. A. Malomed, and T. Huang, “Breather management in the derivative nonlinear Schrödinger equation with variable coefficients,” Ann. Phys. 355(2), 313–321 (2015).
[Crossref]

W. P. Zhong, L. Chen, M. Belić, and N. Petrović, “Controllable parabolic-cylinder optical rogue wave,” Phys. Rev. E 90(4), 043201 (2014).
[Crossref] [PubMed]

W. P. Zhong and M. Belić, “Two-component vector solitons in defocusing Kerr-type media with spatially modulated nonlinearity,” Ann. Phys. 351, 787–796 (2014).
[Crossref]

W. P. Zhong, M. Belić, and T. Huang, “Solitary waves in the nonlinear Schrödinger equation with spatially modulated Bessel nonlinearity,” J. Opt. Soc. Am. B 30(5), 1276–1283 (2013).
[Crossref]

W. P. Zhong, M. Belić, R. H. Xie, G. Chen, and L. Yi, “Two-dimensional Whittaker solitons in nonlocal nonlinear media,” Phys. Rev. A 78(1), 013826 (2008).
[Crossref]

Belic, M. R.

W. P. Zhong, M. R. Belić, and T. Huang, “Rogue wave solutions to the generalized nonlinear Schrödinger equation with variable coefficients,” Phys. Rev. E 87(6), 065201 (2013).
[Crossref] [PubMed]

W. P. Zhong, M. R. Belić, Y. Lu, and T. Huang, “Traveling and solitary wave solutions to the one-dimensional Gross-Pitaevskii equation,” Phys. Rev. E 81(1), 016605 (2010).
[Crossref] [PubMed]

Bendahmane, A.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Bortolozzo, U.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Bree, C.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Broderick, N. G. R.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Chabchoub, A.

A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, “Rogue wave observation in a water wave tank,” Phys. Rev. Lett. 106(20), 204502 (2011).
[Crossref] [PubMed]

Chang, W.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Chen, G.

W. P. Zhong, M. Belić, R. H. Xie, G. Chen, and L. Yi, “Two-dimensional Whittaker solitons in nonlocal nonlinear media,” Phys. Rev. A 78(1), 013826 (2008).
[Crossref]

Chen, L.

W. P. Zhong, L. Chen, M. Belić, and N. Petrović, “Controllable parabolic-cylinder optical rogue wave,” Phys. Rev. E 90(4), 043201 (2014).
[Crossref] [PubMed]

Chen, S.

S. Chen, F. Baronio, J. M. Soto-Crespo, P. Grelu, and D. Mihalache, “Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems,” J. Phys. A Math. Theor. 50(46), 463001 (2017).
[Crossref]

S. Chen, J. M. Soto-Crespo, and P. Grelu, “Dark three-sister rogue waves in normally dispersive optical fibers with random birefringence,” Opt. Express 22(22), 27632–27642 (2014).
[Crossref] [PubMed]

S. Chen and L. Song, “Rogue waves in coupled Hirota systems,” Phys. Rev. E 87(3), 032910 (2013).
[Crossref]

Clamond, D.

D. Clamond, M. Francius, J. Grue, and C. Kharif, “Long time interaction of envelope solitons and freak wave formations,” Eur. J. Mech. BFluids 25(5), 536–553 (2006).
[Crossref]

Coulibaly, S.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Dafilis, M.

A. Toffoli, D. Proment, H. Salman, J. Monbaliu, F. Frascoli, M. Dafilis, E. Stramignoni, R. Forza, M. Manfrin, and M. Onorato, “Wind generated rogue waves in an annular wave flume,” Phys. Rev. Lett. 118(14), 144503 (2017).
[Crossref] [PubMed]

Dai, C.

Z. Yan and C. Dai, “Optical rogue waves in the generalized inhomogeneous higher-order nonlinear Schrödinger equation with modulating coefficients,” J. Opt. 15(6), 064012 (2013).
[Crossref]

Demircan, A.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Dias, F.

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nat. Photonics 8(10), 755–764 (2014).
[Crossref]

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, “Observation of Kuznetsov-Ma soliton dynamics in optical fibre,” Sci. Rep. 2(1), 463 (2012).
[Crossref] [PubMed]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fiber optics,” Nat. Phys. 6(10), 790–795 (2010).
[Crossref]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Express 17(24), 21497–21508 (2009).
[Crossref] [PubMed]

Dudley, J.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Dudley, J. M.

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nat. Photonics 8(10), 755–764 (2014).
[Crossref]

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, “Observation of Kuznetsov-Ma soliton dynamics in optical fibre,” Sci. Rep. 2(1), 463 (2012).
[Crossref] [PubMed]

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, “Rogue wave early warning through spectral measurements,” Phys. Lett. A 375(3), 541–544 (2011).
[Crossref]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
[Crossref] [PubMed]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fiber optics,” Nat. Phys. 6(10), 790–795 (2010).
[Crossref]

G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber super continuum generation in the picosecond regime,” Appl. Phys. B 94(2), 187–194 (2009).
[Crossref]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Express 17(24), 21497–21508 (2009).
[Crossref] [PubMed]

Dysthe, K. B.

K. B. Dysthe and K. Trulsen, “Note on breather type solutions of the NLS as a model for freak-waves,” Phys. Scr. T 82(1), 48–52 (1999).
[Crossref]

Eggleton, B. J.

G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber super continuum generation in the picosecond regime,” Appl. Phys. B 94(2), 187–194 (2009).
[Crossref]

Eleonskii, V.

N. Akhmediev, V. Eleonskii, and N. Kulagin, “Exact first-order solutions of the nonlinear Schrödinger equation,” Theor. Math. Phys. 72(2), 809–818 (1987).
[Crossref]

Erkintalo, M.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nat. Photonics 8(10), 755–764 (2014).
[Crossref]

Fatome, J.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, “Observation of Kuznetsov-Ma soliton dynamics in optical fibre,” Sci. Rep. 2(1), 463 (2012).
[Crossref] [PubMed]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
[Crossref] [PubMed]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fiber optics,” Nat. Phys. 6(10), 790–795 (2010).
[Crossref]

Finot, C.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, “Observation of Kuznetsov-Ma soliton dynamics in optical fibre,” Sci. Rep. 2(1), 463 (2012).
[Crossref] [PubMed]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
[Crossref] [PubMed]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fiber optics,” Nat. Phys. 6(10), 790–795 (2010).
[Crossref]

Forza, R.

A. Toffoli, D. Proment, H. Salman, J. Monbaliu, F. Frascoli, M. Dafilis, E. Stramignoni, R. Forza, M. Manfrin, and M. Onorato, “Wind generated rogue waves in an annular wave flume,” Phys. Rev. Lett. 118(14), 144503 (2017).
[Crossref] [PubMed]

Francius, M.

D. Clamond, M. Francius, J. Grue, and C. Kharif, “Long time interaction of envelope solitons and freak wave formations,” Eur. J. Mech. BFluids 25(5), 536–553 (2006).
[Crossref]

Frascoli, F.

A. Toffoli, D. Proment, H. Salman, J. Monbaliu, F. Frascoli, M. Dafilis, E. Stramignoni, R. Forza, M. Manfrin, and M. Onorato, “Wind generated rogue waves in an annular wave flume,” Phys. Rev. Lett. 118(14), 144503 (2017).
[Crossref] [PubMed]

Gaillard, P.

P. Gaillard, “Deformations of third-order Peregrine breather solutions of the nonlinear Schrödinger equation with four parameters,” Phys. Rev. E 88(4), 042903 (2013).
[Crossref] [PubMed]

Genty, G.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nat. Photonics 8(10), 755–764 (2014).
[Crossref]

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, “Observation of Kuznetsov-Ma soliton dynamics in optical fibre,” Sci. Rep. 2(1), 463 (2012).
[Crossref] [PubMed]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fiber optics,” Nat. Phys. 6(10), 790–795 (2010).
[Crossref]

G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber super continuum generation in the picosecond regime,” Appl. Phys. B 94(2), 187–194 (2009).
[Crossref]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Express 17(24), 21497–21508 (2009).
[Crossref] [PubMed]

Grelu, P.

S. Chen, F. Baronio, J. M. Soto-Crespo, P. Grelu, and D. Mihalache, “Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems,” J. Phys. A Math. Theor. 50(46), 463001 (2017).
[Crossref]

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
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S. Chen, J. M. Soto-Crespo, and P. Grelu, “Dark three-sister rogue waves in normally dispersive optical fibers with random birefringence,” Opt. Express 22(22), 27632–27642 (2014).
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Grue, J.

D. Clamond, M. Francius, J. Grue, and C. Kharif, “Long time interaction of envelope solitons and freak wave formations,” Eur. J. Mech. BFluids 25(5), 536–553 (2006).
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Hammani, K.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
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K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
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He, J.

J. Zhou, H. Li, and J. He, “Analytical periodic wave and soliton solutions of the generalized nonautonomous nonlinear Schrödinger equation in harmonic and optical lattice potentials,” Commum. Theor. Phys. 58(3), 393–397 (2012).
[Crossref]

J. He, S. Xu, and K. Porsezian, “N-order bright and dark rogue waves in a resonant erbium-doped fiber system,” Phys. Rev. E 86(6), 066603 (2012).
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He, J. R.

J. R. He and H. M. Li, “Analytical solitary-wave solutions of the generalized nonautonomous cubic-quintic nonlinear Schrödinger equation with different external potentials,” Phys. Rev. E 83(6), 066607 (2011).
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D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6(7), 463–468 (2012).
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Hoffmann, N. P.

A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, “Rogue wave observation in a water wave tank,” Phys. Rev. Lett. 106(20), 204502 (2011).
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Huang, T.

W. P. Zhong, M. Belić, B. A. Malomed, and T. Huang, “Breather management in the derivative nonlinear Schrödinger equation with variable coefficients,” Ann. Phys. 355(2), 313–321 (2015).
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W. P. Zhong, M. R. Belić, and T. Huang, “Rogue wave solutions to the generalized nonlinear Schrödinger equation with variable coefficients,” Phys. Rev. E 87(6), 065201 (2013).
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W. P. Zhong, M. Belić, and T. Huang, “Solitary waves in the nonlinear Schrödinger equation with spatially modulated Bessel nonlinearity,” J. Opt. Soc. Am. B 30(5), 1276–1283 (2013).
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W. P. Zhong, M. R. Belić, Y. Lu, and T. Huang, “Traveling and solitary wave solutions to the one-dimensional Gross-Pitaevskii equation,” Phys. Rev. E 81(1), 016605 (2010).
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D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6(7), 463–468 (2012).
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D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
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D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Classifying the hierarchy of nonlinear-Schrödinger-equation rogue-wave solutions,” Phys. Rev. E 88(1), 013207 (2013).
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D. Clamond, M. Francius, J. Grue, and C. Kharif, “Long time interaction of envelope solitons and freak wave formations,” Eur. J. Mech. BFluids 25(5), 536–553 (2006).
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N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
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B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, “Observation of Kuznetsov-Ma soliton dynamics in optical fibre,” Sci. Rep. 2(1), 463 (2012).
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K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
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B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fiber optics,” Nat. Phys. 6(10), 790–795 (2010).
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J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Express 17(24), 21497–21508 (2009).
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Koonath, P.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
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N. N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrödinger equation,” Theor. Math. Phys. 69(2), 1089–1093 (1986).
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N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
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N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
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J. Zhou, H. Li, and J. He, “Analytical periodic wave and soliton solutions of the generalized nonautonomous nonlinear Schrödinger equation in harmonic and optical lattice potentials,” Commum. Theor. Phys. 58(3), 393–397 (2012).
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Li, H. M.

J. R. He and H. M. Li, “Analytical solitary-wave solutions of the generalized nonautonomous cubic-quintic nonlinear Schrödinger equation with different external potentials,” Phys. Rev. E 83(6), 066607 (2011).
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D. Liang, Z. Yang, C. Liu, and W. Yang, “Optical rogue wave excitation and modulation on a bright soliton background,” Chin. Phys. Lett. 33(1), 010501 (2016).
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W. P. Zhong, M. R. Belić, Y. Lu, and T. Huang, “Traveling and solitary wave solutions to the one-dimensional Gross-Pitaevskii equation,” Phys. Rev. E 81(1), 016605 (2010).
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W. P. Zhong, M. Belić, B. A. Malomed, and T. Huang, “Breather management in the derivative nonlinear Schrödinger equation with variable coefficients,” Ann. Phys. 355(2), 313–321 (2015).
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A. Toffoli, D. Proment, H. Salman, J. Monbaliu, F. Frascoli, M. Dafilis, E. Stramignoni, R. Forza, M. Manfrin, and M. Onorato, “Wind generated rogue waves in an annular wave flume,” Phys. Rev. Lett. 118(14), 144503 (2017).
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N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Mihalache, D.

S. Chen, F. Baronio, J. M. Soto-Crespo, P. Grelu, and D. Mihalache, “Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems,” J. Phys. A Math. Theor. 50(46), 463001 (2017).
[Crossref]

Millot, G.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, “Observation of Kuznetsov-Ma soliton dynamics in optical fibre,” Sci. Rep. 2(1), 463 (2012).
[Crossref] [PubMed]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
[Crossref] [PubMed]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fiber optics,” Nat. Phys. 6(10), 790–795 (2010).
[Crossref]

Monbaliu, J.

A. Toffoli, D. Proment, H. Salman, J. Monbaliu, F. Frascoli, M. Dafilis, E. Stramignoni, R. Forza, M. Manfrin, and M. Onorato, “Wind generated rogue waves in an annular wave flume,” Phys. Rev. Lett. 118(14), 144503 (2017).
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N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
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N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
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Y. Ohta and J. Yang, “Rogue waves in the Davey-Stewartson I equation,” Phys. Rev. E 86(3), 036604 (2012).
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A. Toffoli, D. Proment, H. Salman, J. Monbaliu, F. Frascoli, M. Dafilis, E. Stramignoni, R. Forza, M. Manfrin, and M. Onorato, “Wind generated rogue waves in an annular wave flume,” Phys. Rev. Lett. 118(14), 144503 (2017).
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Panajotov, K.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
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W. P. Zhong, L. Chen, M. Belić, and N. Petrović, “Controllable parabolic-cylinder optical rogue wave,” Phys. Rev. E 90(4), 043201 (2014).
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Picozzi, A.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
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Porsezian, K.

J. He, S. Xu, and K. Porsezian, “N-order bright and dark rogue waves in a resonant erbium-doped fiber system,” Phys. Rev. E 86(6), 066603 (2012).
[Crossref] [PubMed]

Proment, D.

A. Toffoli, D. Proment, H. Salman, J. Monbaliu, F. Frascoli, M. Dafilis, E. Stramignoni, R. Forza, M. Manfrin, and M. Onorato, “Wind generated rogue waves in an annular wave flume,” Phys. Rev. Lett. 118(14), 144503 (2017).
[Crossref] [PubMed]

Residori, S.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
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Rica, S.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
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D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6(7), 463–468 (2012).
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D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
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Runge, A. F. J.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
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Salman, H.

A. Toffoli, D. Proment, H. Salman, J. Monbaliu, F. Frascoli, M. Dafilis, E. Stramignoni, R. Forza, M. Manfrin, and M. Onorato, “Wind generated rogue waves in an annular wave flume,” Phys. Rev. Lett. 118(14), 144503 (2017).
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D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6(7), 463–468 (2012).
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D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
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S. Chen, F. Baronio, J. M. Soto-Crespo, P. Grelu, and D. Mihalache, “Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems,” J. Phys. A Math. Theor. 50(46), 463001 (2017).
[Crossref]

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

S. Chen, J. M. Soto-Crespo, and P. Grelu, “Dark three-sister rogue waves in normally dispersive optical fibers with random birefringence,” Opt. Express 22(22), 27632–27642 (2014).
[Crossref] [PubMed]

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, “Rogue wave early warning through spectral measurements,” Phys. Lett. A 375(3), 541–544 (2011).
[Crossref]

A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Rogue waves and rational solutions of the Hirota equation,” Phys. Rev. E 81(4), 046602 (2010).
[Crossref] [PubMed]

N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Rogue waves and rational solutions of the nonlinear Schrödinger equation,” Phys. Rev. E 80(2), 026601 (2009).
[Crossref] [PubMed]

Steinmeyer, G.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Stramignoni, E.

A. Toffoli, D. Proment, H. Salman, J. Monbaliu, F. Frascoli, M. Dafilis, E. Stramignoni, R. Forza, M. Manfrin, and M. Onorato, “Wind generated rogue waves in an annular wave flume,” Phys. Rev. Lett. 118(14), 144503 (2017).
[Crossref] [PubMed]

Szriftgiser, P.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Taki, M.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Thomas, G.

V. V. Voronovich, V. I. Shrira, and G. Thomas, “Can bottom friction suppress ‘freak wave’ formation?” J. Fluid Mech. 604(2), 263–296 (2008).

Tiofack, C. G.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Tlidi, M.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Toffoli, A.

A. Toffoli, D. Proment, H. Salman, J. Monbaliu, F. Frascoli, M. Dafilis, E. Stramignoni, R. Forza, M. Manfrin, and M. Onorato, “Wind generated rogue waves in an annular wave flume,” Phys. Rev. Lett. 118(14), 144503 (2017).
[Crossref] [PubMed]

Trulsen, K.

K. B. Dysthe and K. Trulsen, “Note on breather type solutions of the NLS as a model for freak-waves,” Phys. Scr. T 82(1), 48–52 (1999).
[Crossref]

Voronovich, V. V.

V. V. Voronovich, V. I. Shrira, and G. Thomas, “Can bottom friction suppress ‘freak wave’ formation?” J. Fluid Mech. 604(2), 263–296 (2008).

Vouzas, P.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Wabnitz, S.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Wen, L.

X. Zhang, L. Wen, X. Luo, and Z. Xie, “Exact solutions of the generalized nonlinear Schrödinger equation with time- and space-modulated coefficients,” Phys. Lett. A 376(11), 465–468 (2012).
[Crossref]

Wetzel, B.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, “Observation of Kuznetsov-Ma soliton dynamics in optical fibre,” Sci. Rep. 2(1), 463 (2012).
[Crossref] [PubMed]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
[Crossref] [PubMed]

Xie, R. H.

W. P. Zhong, M. Belić, R. H. Xie, G. Chen, and L. Yi, “Two-dimensional Whittaker solitons in nonlocal nonlinear media,” Phys. Rev. A 78(1), 013826 (2008).
[Crossref]

Xie, Z.

X. Zhang, L. Wen, X. Luo, and Z. Xie, “Exact solutions of the generalized nonlinear Schrödinger equation with time- and space-modulated coefficients,” Phys. Lett. A 376(11), 465–468 (2012).
[Crossref]

Xu, S.

J. He, S. Xu, and K. Porsezian, “N-order bright and dark rogue waves in a resonant erbium-doped fiber system,” Phys. Rev. E 86(6), 066603 (2012).
[Crossref] [PubMed]

Yan, Z.

Z. Yan and C. Dai, “Optical rogue waves in the generalized inhomogeneous higher-order nonlinear Schrödinger equation with modulating coefficients,” J. Opt. 15(6), 064012 (2013).
[Crossref]

Z. Yan, “Nonautonomous ‘rogons’ in the inhomogeneous nonlinear Schrödinger equation with variable coefficients,” Phys. Lett. 374(4), 672–679 (2010).
[Crossref]

Yang, J.

Y. Ohta and J. Yang, “Rogue waves in the Davey-Stewartson I equation,” Phys. Rev. E 86(3), 036604 (2012).
[Crossref] [PubMed]

Yang, W.

D. Liang, Z. Yang, C. Liu, and W. Yang, “Optical rogue wave excitation and modulation on a bright soliton background,” Chin. Phys. Lett. 33(1), 010501 (2016).
[Crossref]

Yang, Z.

D. Liang, Z. Yang, C. Liu, and W. Yang, “Optical rogue wave excitation and modulation on a bright soliton background,” Chin. Phys. Lett. 33(1), 010501 (2016).
[Crossref]

Yi, L.

W. P. Zhong, M. Belić, R. H. Xie, G. Chen, and L. Yi, “Two-dimensional Whittaker solitons in nonlocal nonlinear media,” Phys. Rev. A 78(1), 013826 (2008).
[Crossref]

Zhang, X.

X. Zhang, L. Wen, X. Luo, and Z. Xie, “Exact solutions of the generalized nonlinear Schrödinger equation with time- and space-modulated coefficients,” Phys. Lett. A 376(11), 465–468 (2012).
[Crossref]

Zhang, Y.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

M. Belić, W. P. Zhong, and Y. Zhang, “Predictable rogue waves,” J. Opt. 18, 063001 (2016).

Zhao, L. C.

L. Ling and L. C. Zhao, “Simple determinant representation for rogue waves of the nonlinear Schrödinger equation,” Phys. Rev. E 88(4), 043201 (2013).
[Crossref] [PubMed]

Zhong, W. P.

M. Belić, W. P. Zhong, and Y. Zhang, “Predictable rogue waves,” J. Opt. 18, 063001 (2016).

W. P. Zhong, M. Belić, B. A. Malomed, and T. Huang, “Breather management in the derivative nonlinear Schrödinger equation with variable coefficients,” Ann. Phys. 355(2), 313–321 (2015).
[Crossref]

W. P. Zhong and M. Belić, “Two-component vector solitons in defocusing Kerr-type media with spatially modulated nonlinearity,” Ann. Phys. 351, 787–796 (2014).
[Crossref]

W. P. Zhong, L. Chen, M. Belić, and N. Petrović, “Controllable parabolic-cylinder optical rogue wave,” Phys. Rev. E 90(4), 043201 (2014).
[Crossref] [PubMed]

W. P. Zhong, M. R. Belić, and T. Huang, “Rogue wave solutions to the generalized nonlinear Schrödinger equation with variable coefficients,” Phys. Rev. E 87(6), 065201 (2013).
[Crossref] [PubMed]

W. P. Zhong, M. Belić, and T. Huang, “Solitary waves in the nonlinear Schrödinger equation with spatially modulated Bessel nonlinearity,” J. Opt. Soc. Am. B 30(5), 1276–1283 (2013).
[Crossref]

W. P. Zhong, “Rogue wave solutions of the generalized one-dimensional Gross-Pitaevskii equation,” J. Nonlinear Opt. Phys. Mater. 21(02), 1250026 (2012).
[Crossref]

W. P. Zhong, M. R. Belić, Y. Lu, and T. Huang, “Traveling and solitary wave solutions to the one-dimensional Gross-Pitaevskii equation,” Phys. Rev. E 81(1), 016605 (2010).
[Crossref] [PubMed]

W. P. Zhong, M. Belić, R. H. Xie, G. Chen, and L. Yi, “Two-dimensional Whittaker solitons in nonlocal nonlinear media,” Phys. Rev. A 78(1), 013826 (2008).
[Crossref]

Zhong, W.-P.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

Zhou, J.

J. Zhou, H. Li, and J. He, “Analytical periodic wave and soliton solutions of the generalized nonautonomous nonlinear Schrödinger equation in harmonic and optical lattice potentials,” Commum. Theor. Phys. 58(3), 393–397 (2012).
[Crossref]

Ann. Phys. (2)

W. P. Zhong, M. Belić, B. A. Malomed, and T. Huang, “Breather management in the derivative nonlinear Schrödinger equation with variable coefficients,” Ann. Phys. 355(2), 313–321 (2015).
[Crossref]

W. P. Zhong and M. Belić, “Two-component vector solitons in defocusing Kerr-type media with spatially modulated nonlinearity,” Ann. Phys. 351, 787–796 (2014).
[Crossref]

Appl. Phys. B (1)

G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber super continuum generation in the picosecond regime,” Appl. Phys. B 94(2), 187–194 (2009).
[Crossref]

Chin. Phys. Lett. (1)

D. Liang, Z. Yang, C. Liu, and W. Yang, “Optical rogue wave excitation and modulation on a bright soliton background,” Chin. Phys. Lett. 33(1), 010501 (2016).
[Crossref]

Commum. Theor. Phys. (1)

J. Zhou, H. Li, and J. He, “Analytical periodic wave and soliton solutions of the generalized nonautonomous nonlinear Schrödinger equation in harmonic and optical lattice potentials,” Commum. Theor. Phys. 58(3), 393–397 (2012).
[Crossref]

Eur. J. Mech. BFluids (1)

D. Clamond, M. Francius, J. Grue, and C. Kharif, “Long time interaction of envelope solitons and freak wave formations,” Eur. J. Mech. BFluids 25(5), 536–553 (2006).
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Eur. Phys. J. (1)

N. Akhmediev and E. Pelinovsky, “Introductory remarks on “Discussion & Debate: Rogue Waves – Towards a Unifying Concept?” Eur. Phys. J. 185(1), 1–4 (2010).

J. Fluid Mech. (1)

V. V. Voronovich, V. I. Shrira, and G. Thomas, “Can bottom friction suppress ‘freak wave’ formation?” J. Fluid Mech. 604(2), 263–296 (2008).

J. Nonlinear Opt. Phys. Mater. (1)

W. P. Zhong, “Rogue wave solutions of the generalized one-dimensional Gross-Pitaevskii equation,” J. Nonlinear Opt. Phys. Mater. 21(02), 1250026 (2012).
[Crossref]

J. Opt. (3)

Z. Yan and C. Dai, “Optical rogue waves in the generalized inhomogeneous higher-order nonlinear Schrödinger equation with modulating coefficients,” J. Opt. 15(6), 064012 (2013).
[Crossref]

M. Belić, W. P. Zhong, and Y. Zhang, “Predictable rogue waves,” J. Opt. 18, 063001 (2016).

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(4), 063001 (2016).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. A Math. Theor. (1)

S. Chen, F. Baronio, J. M. Soto-Crespo, P. Grelu, and D. Mihalache, “Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems,” J. Phys. A Math. Theor. 50(46), 463001 (2017).
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Nat. Photonics (2)

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6(7), 463–468 (2012).
[Crossref]

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nat. Photonics 8(10), 755–764 (2014).
[Crossref]

Nat. Phys. (1)

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fiber optics,” Nat. Phys. 6(10), 790–795 (2010).
[Crossref]

Nature (1)

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

Phys. Lett. (1)

Z. Yan, “Nonautonomous ‘rogons’ in the inhomogeneous nonlinear Schrödinger equation with variable coefficients,” Phys. Lett. 374(4), 672–679 (2010).
[Crossref]

Phys. Lett. A (2)

X. Zhang, L. Wen, X. Luo, and Z. Xie, “Exact solutions of the generalized nonlinear Schrödinger equation with time- and space-modulated coefficients,” Phys. Lett. A 376(11), 465–468 (2012).
[Crossref]

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, “Rogue wave early warning through spectral measurements,” Phys. Lett. A 375(3), 541–544 (2011).
[Crossref]

Phys. Rev. A (1)

W. P. Zhong, M. Belić, R. H. Xie, G. Chen, and L. Yi, “Two-dimensional Whittaker solitons in nonlocal nonlinear media,” Phys. Rev. A 78(1), 013826 (2008).
[Crossref]

Phys. Rev. E (12)

W. P. Zhong, L. Chen, M. Belić, and N. Petrović, “Controllable parabolic-cylinder optical rogue wave,” Phys. Rev. E 90(4), 043201 (2014).
[Crossref] [PubMed]

P. Gaillard, “Deformations of third-order Peregrine breather solutions of the nonlinear Schrödinger equation with four parameters,” Phys. Rev. E 88(4), 042903 (2013).
[Crossref] [PubMed]

L. Ling and L. C. Zhao, “Simple determinant representation for rogue waves of the nonlinear Schrödinger equation,” Phys. Rev. E 88(4), 043201 (2013).
[Crossref] [PubMed]

D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Classifying the hierarchy of nonlinear-Schrödinger-equation rogue-wave solutions,” Phys. Rev. E 88(1), 013207 (2013).
[Crossref] [PubMed]

J. He, S. Xu, and K. Porsezian, “N-order bright and dark rogue waves in a resonant erbium-doped fiber system,” Phys. Rev. E 86(6), 066603 (2012).
[Crossref] [PubMed]

W. P. Zhong, M. R. Belić, Y. Lu, and T. Huang, “Traveling and solitary wave solutions to the one-dimensional Gross-Pitaevskii equation,” Phys. Rev. E 81(1), 016605 (2010).
[Crossref] [PubMed]

J. R. He and H. M. Li, “Analytical solitary-wave solutions of the generalized nonautonomous cubic-quintic nonlinear Schrödinger equation with different external potentials,” Phys. Rev. E 83(6), 066607 (2011).
[Crossref] [PubMed]

N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Rogue waves and rational solutions of the nonlinear Schrödinger equation,” Phys. Rev. E 80(2), 026601 (2009).
[Crossref] [PubMed]

W. P. Zhong, M. R. Belić, and T. Huang, “Rogue wave solutions to the generalized nonlinear Schrödinger equation with variable coefficients,” Phys. Rev. E 87(6), 065201 (2013).
[Crossref] [PubMed]

A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Rogue waves and rational solutions of the Hirota equation,” Phys. Rev. E 81(4), 046602 (2010).
[Crossref] [PubMed]

S. Chen and L. Song, “Rogue waves in coupled Hirota systems,” Phys. Rev. E 87(3), 032910 (2013).
[Crossref]

Y. Ohta and J. Yang, “Rogue waves in the Davey-Stewartson I equation,” Phys. Rev. E 86(3), 036604 (2012).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, “Rogue wave observation in a water wave tank,” Phys. Rev. Lett. 106(20), 204502 (2011).
[Crossref] [PubMed]

A. Toffoli, D. Proment, H. Salman, J. Monbaliu, F. Frascoli, M. Dafilis, E. Stramignoni, R. Forza, M. Manfrin, and M. Onorato, “Wind generated rogue waves in an annular wave flume,” Phys. Rev. Lett. 118(14), 144503 (2017).
[Crossref] [PubMed]

Phys. Scr. T (1)

K. B. Dysthe and K. Trulsen, “Note on breather type solutions of the NLS as a model for freak-waves,” Phys. Scr. T 82(1), 48–52 (1999).
[Crossref]

Sci. Rep. (1)

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, “Observation of Kuznetsov-Ma soliton dynamics in optical fibre,” Sci. Rep. 2(1), 463 (2012).
[Crossref] [PubMed]

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D. H. Peregrine, “Water waves, nonlinear Schrödinger equations and their solutions,” Soc. Ser. B: Appl. Math. 25(1), 16–43 (1983).

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Figures (7)

Fig. 1
Fig. 1 First-order rogue waves. (a) Peregrine soliton. (b)-(d) Managed Akhmediev-like breathers. The parameters are given in the text.
Fig. 2
Fig. 2 Standard second-order rogue wave solutions with s1 = 0. (a) Maximum-peak second-order rogue wave. (b)-(d) Managed maximum-peak second-order rogue waves. Other parameters are given in the text.
Fig. 3
Fig. 3 Second-order rogue wave structures with the parameter s 1 =10i. (a) The standard second-order rogue wave without management. (b) Managed second-order dark rogue wave. Other parameters are given in the text.
Fig. 4
Fig. 4 Third-order rogue wave solutions. (a) The standard maximum-height third-order rogue wave solution. (b)-(d) Managed maximum-height third-order rogue wave solutions. The parameters are given in the text.
Fig. 5
Fig. 5 Third-order rogue waves with two real parameters s 1 = s 2 =50 (top row) and s 1 =1, s 2 =5000 (bottom row); Left column: without the nonlinearity management, right column: with the nonlinearity management.
Fig. 6
Fig. 6 Third-order rogue waves with imaginary parameters. Parameters are given in the text, and the setup is the same as in Fig. 5.
Fig. 7
Fig. 7 Dark breather profiles as computed from Eq. (6) under the perturbation with 10% initial white noise. The parameters are the same as in Figs. 3(b) and 5(a), the right panel.

Equations (13)

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i u z +β( x,z ) 2 u x 2 +2χ( x,z ) | u | 2 u=U( x,z )u ,
i V z + 2 V X 2 +2 | V | 2 V=0 ,
u( z,x )=V( z,X ) e A( z,x )+iB( z,x ) ,
β ( X x ) 2 =1 , χ e 2A =1
x ( e 2A X x )=0 , B z +β[ A xx + ( A x ) 2 ( B x ) 2 ]=U ,
B x = 1 2β X z X x , z e 2A +2β x ( e 2A B x )=0 .
X=λ( z )F( x )+θ( z ) ,
A= 1 2 ln λ( z ) F x ( x ) ,
B( z,x )= 1 4 λ λ z F 2 1 2 λ θ z F+ω( z ) .
U= 1 4 λ λ zz F 2 + 1 2 λ θ zz F 1 4 θ z 2 + ω z ( z )+ 3 F xx 2 2 F x F xx 4 λ 2 F x 4 ,
F( z,x )=λ( z ) χ( z,x )dx ,
u( z,x )= λ F x V( z,X ) e i[ λ λ z 4 F 2 λ θ z 2 F+ω( z ) ] .
λ( z )=1+Acos( Ωz ) , θ( z )=acos( ωz ) ,

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