Abstract

An approximate analytical solution of the non-integrable problem of steady-state adiabatic interaction of a cnoidal wave with a breather is obtained. The solving algorithm is described by the example of one-dimensional problem of steady-state interaction of a plane cnoidal wave with circular polarization (the “information” signal) with orthogonally polarized rational soliton (the “control” signal) in an isotropic nonlinear gyrotropic medium with Kerr nonlinearity and second-order group-velocity dispersion. It is shown that such the interaction results in a strong amplitude and frequency modulation of the information signal and this modulation is localized in the region where intensity of the control signal changes.

© 2014 Optical Society of America

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References

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  6. C. Kalla, “Breathers and solitons of generalized nonlinear Schrödinger equations as degenerations of algebro-geometric solutions,” J. Phys. A: Math. Theor. 44(33), 335210 (2011).
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  7. X. R. Hu, S. Y. Lou, and Y. Chen, “Explicit solutions from eigenfunction symmetry of the Korteweg-de Vries equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(5), 056607 (2012).
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    [Crossref] [PubMed]
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2014 (6)

F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, and S. Wabnitz, “Vector rogue waves and baseband modulation instability in the defocusing regime,” Phys. Rev. Lett. 113(3), 034101 (2014).
[Crossref] [PubMed]

X. P. Cheng, S. Y. Lou, C. L. Chen, and X. Y. Tang, “Interactions between solitons and other nonlinear Schrödinger waves,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 89(4), 043202 (2014).
[Crossref] [PubMed]

O. V. Yushko and A. A. Redyuk, “Soliton communication lines based on spectrally efficient modulation formats,” Quantum Electron. 44(6), 606–611 (2014).
[Crossref]

W. Cai, M. S. Mills, D. N. Christodoulides, and S. Wen, “Soliton manipulation using Airy pulses,” Opt. Commun. 316, 127–131 (2014).
[Crossref]

V. A. Makarov, V. M. Petnikova, N. N. Potravkin, and V. V. Shuvalov, “Approximate solutions to a nonintegrable problem of propagation of elliptically polarized waves in an isotropic gyrotropic nonlinear medium, and periodic analogues of multisoliton complexes,” Quantum Electron. 44(2), 130–134 (2014).
[Crossref]

V. A. Makarov, V. M. Petnikova, and V. V. Shuvalov, “Adiabatic approximation and aperiodic dynamics of an elliptically polarized light wave in an isotropic gyrotropic nonlinear medium,” Laser Phys. 24(8), 085405 (2014).
[Crossref]

2013 (2)

L. C. Zhao and J. Liu, “Rogue-wave solutions of a three-component coupled nonlinear Schrödinger equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 87(1), 013201 (2013).
[Crossref] [PubMed]

B. G. Zhai, W. G. Zhang, X. L. Wang, and H. Q. Zhang, “Multi-rogue waves and rational solutions of the coupled nonlinear Schrödinger equations,” Nonlinear Anal. Real World Appl. 14(1), 14–27 (2013).
[Crossref]

2012 (3)

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[Crossref] [PubMed]

X. R. Hu, S. Y. Lou, and Y. Chen, “Explicit solutions from eigenfunction symmetry of the Korteweg-de Vries equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(5), 056607 (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, 463 (2012).
[Crossref] [PubMed]

2011 (1)

C. Kalla, “Breathers and solitons of generalized nonlinear Schrödinger equations as degenerations of algebro-geometric solutions,” J. Phys. A: Math. Theor. 44(33), 335210 (2011).
[Crossref]

2010 (2)

Yu. V. Bludov, V. V. Konotop, and N. Akhmediev, “Vector rogue waves in binary mixtures of Bose-Einstein condensates,” Eur. Phys. J. Spec. Top. 185(1), 169–180 (2010).
[Crossref]

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

2007 (1)

V. M. Petnikova and V. V. Shuvalov, “Parametric frequency conversion, nonlinear Schrödinger equation, and multicomponent cnoidal waves,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046611 (2007).
[Crossref] [PubMed]

2003 (1)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

2002 (1)

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “All-optical switching and logic gating with spatial solitons in liquid crystals,” Appl. Phys. Lett. 81(18), 3335–3337 (2002).
[Crossref]

2000 (2)

P. L. Christiansen, J. C. Eilbeck, V. Z. Enolskii, and N. A. Kostov, “Quasi-periodic and periodic solutions for Manakov type systems of coupled nonlinear Schrodinger equations,” Proc. R. Soc. Lond. A 456, 2263–2281 (2000).
[Crossref]

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, “Recent progress in soliton transmission technology,” Chaos 10(3), 486–514 (2000).
[Crossref] [PubMed]

Akhmediev, N.

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, 463 (2012).
[Crossref] [PubMed]

Yu. V. Bludov, V. V. Konotop, and N. Akhmediev, “Vector rogue waves in binary mixtures of Bose-Einstein condensates,” Eur. Phys. J. Spec. Top. 185(1), 169–180 (2010).
[Crossref]

Akhmediev, N. N.

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

Assanto, G.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “All-optical switching and logic gating with spatial solitons in liquid crystals,” Appl. Phys. Lett. 81(18), 3335–3337 (2002).
[Crossref]

Baronio, F.

F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, and S. Wabnitz, “Vector rogue waves and baseband modulation instability in the defocusing regime,” Phys. Rev. Lett. 113(3), 034101 (2014).
[Crossref] [PubMed]

Bludov, Yu. V.

Yu. V. Bludov, V. V. Konotop, and N. Akhmediev, “Vector rogue waves in binary mixtures of Bose-Einstein condensates,” Eur. Phys. J. Spec. Top. 185(1), 169–180 (2010).
[Crossref]

Cai, W.

W. Cai, M. S. Mills, D. N. Christodoulides, and S. Wen, “Soliton manipulation using Airy pulses,” Opt. Commun. 316, 127–131 (2014).
[Crossref]

Chen, C. L.

X. P. Cheng, S. Y. Lou, C. L. Chen, and X. Y. Tang, “Interactions between solitons and other nonlinear Schrödinger waves,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 89(4), 043202 (2014).
[Crossref] [PubMed]

Chen, Y.

X. R. Hu, S. Y. Lou, and Y. Chen, “Explicit solutions from eigenfunction symmetry of the Korteweg-de Vries equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(5), 056607 (2012).
[Crossref] [PubMed]

Chen, Z.

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[Crossref] [PubMed]

Cheng, X. P.

X. P. Cheng, S. Y. Lou, C. L. Chen, and X. Y. Tang, “Interactions between solitons and other nonlinear Schrödinger waves,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 89(4), 043202 (2014).
[Crossref] [PubMed]

Christiansen, P. L.

P. L. Christiansen, J. C. Eilbeck, V. Z. Enolskii, and N. A. Kostov, “Quasi-periodic and periodic solutions for Manakov type systems of coupled nonlinear Schrodinger equations,” Proc. R. Soc. Lond. A 456, 2263–2281 (2000).
[Crossref]

Christodoulides, D. N.

W. Cai, M. S. Mills, D. N. Christodoulides, and S. Wen, “Soliton manipulation using Airy pulses,” Opt. Commun. 316, 127–131 (2014).
[Crossref]

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[Crossref] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

Conforti, M.

F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, and S. Wabnitz, “Vector rogue waves and baseband modulation instability in the defocusing regime,” Phys. Rev. Lett. 113(3), 034101 (2014).
[Crossref] [PubMed]

Conti, C.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “All-optical switching and logic gating with spatial solitons in liquid crystals,” Appl. Phys. Lett. 81(18), 3335–3337 (2002).
[Crossref]

De Luca, A.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “All-optical switching and logic gating with spatial solitons in liquid crystals,” Appl. Phys. Lett. 81(18), 3335–3337 (2002).
[Crossref]

Degasperis, A.

F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, and S. Wabnitz, “Vector rogue waves and baseband modulation instability in the defocusing regime,” Phys. Rev. Lett. 113(3), 034101 (2014).
[Crossref] [PubMed]

Dias, F.

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, 463 (2012).
[Crossref] [PubMed]

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

Dudley, J. M.

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, 463 (2012).
[Crossref] [PubMed]

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

Eilbeck, J. C.

P. L. Christiansen, J. C. Eilbeck, V. Z. Enolskii, and N. A. Kostov, “Quasi-periodic and periodic solutions for Manakov type systems of coupled nonlinear Schrodinger equations,” Proc. R. Soc. Lond. A 456, 2263–2281 (2000).
[Crossref]

Enolskii, V. Z.

P. L. Christiansen, J. C. Eilbeck, V. Z. Enolskii, and N. A. Kostov, “Quasi-periodic and periodic solutions for Manakov type systems of coupled nonlinear Schrodinger equations,” Proc. R. Soc. Lond. A 456, 2263–2281 (2000).
[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, 463 (2012).
[Crossref] [PubMed]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre 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, 463 (2012).
[Crossref] [PubMed]

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

Genty, 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, 463 (2012).
[Crossref] [PubMed]

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

Hu, X. R.

X. R. Hu, S. Y. Lou, and Y. Chen, “Explicit solutions from eigenfunction symmetry of the Korteweg-de Vries equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(5), 056607 (2012).
[Crossref] [PubMed]

Kalla, C.

C. Kalla, “Breathers and solitons of generalized nonlinear Schrödinger equations as degenerations of algebro-geometric solutions,” J. Phys. A: Math. Theor. 44(33), 335210 (2011).
[Crossref]

Kibler, 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, 463 (2012).
[Crossref] [PubMed]

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

Konotop, V. V.

Yu. V. Bludov, V. V. Konotop, and N. Akhmediev, “Vector rogue waves in binary mixtures of Bose-Einstein condensates,” Eur. Phys. J. Spec. Top. 185(1), 169–180 (2010).
[Crossref]

Kostov, N. A.

P. L. Christiansen, J. C. Eilbeck, V. Z. Enolskii, and N. A. Kostov, “Quasi-periodic and periodic solutions for Manakov type systems of coupled nonlinear Schrodinger equations,” Proc. R. Soc. Lond. A 456, 2263–2281 (2000).
[Crossref]

Kubota, H.

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, “Recent progress in soliton transmission technology,” Chaos 10(3), 486–514 (2000).
[Crossref] [PubMed]

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

Liu, J.

L. C. Zhao and J. Liu, “Rogue-wave solutions of a three-component coupled nonlinear Schrödinger equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 87(1), 013201 (2013).
[Crossref] [PubMed]

Lombardo, S.

F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, and S. Wabnitz, “Vector rogue waves and baseband modulation instability in the defocusing regime,” Phys. Rev. Lett. 113(3), 034101 (2014).
[Crossref] [PubMed]

Lou, S. Y.

X. P. Cheng, S. Y. Lou, C. L. Chen, and X. Y. Tang, “Interactions between solitons and other nonlinear Schrödinger waves,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 89(4), 043202 (2014).
[Crossref] [PubMed]

X. R. Hu, S. Y. Lou, and Y. Chen, “Explicit solutions from eigenfunction symmetry of the Korteweg-de Vries equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(5), 056607 (2012).
[Crossref] [PubMed]

Makarov, V. A.

V. A. Makarov, V. M. Petnikova, N. N. Potravkin, and V. V. Shuvalov, “Approximate solutions to a nonintegrable problem of propagation of elliptically polarized waves in an isotropic gyrotropic nonlinear medium, and periodic analogues of multisoliton complexes,” Quantum Electron. 44(2), 130–134 (2014).
[Crossref]

V. A. Makarov, V. M. Petnikova, and V. V. Shuvalov, “Adiabatic approximation and aperiodic dynamics of an elliptically polarized light wave in an isotropic gyrotropic nonlinear medium,” Laser Phys. 24(8), 085405 (2014).
[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, 463 (2012).
[Crossref] [PubMed]

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

Mills, M. S.

W. Cai, M. S. Mills, D. N. Christodoulides, and S. Wen, “Soliton manipulation using Airy pulses,” Opt. Commun. 316, 127–131 (2014).
[Crossref]

Nakazawa, M.

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, “Recent progress in soliton transmission technology,” Chaos 10(3), 486–514 (2000).
[Crossref] [PubMed]

Onorato, M.

F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, and S. Wabnitz, “Vector rogue waves and baseband modulation instability in the defocusing regime,” Phys. Rev. Lett. 113(3), 034101 (2014).
[Crossref] [PubMed]

Peccianti, M.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “All-optical switching and logic gating with spatial solitons in liquid crystals,” Appl. Phys. Lett. 81(18), 3335–3337 (2002).
[Crossref]

Petnikova, V. M.

V. A. Makarov, V. M. Petnikova, N. N. Potravkin, and V. V. Shuvalov, “Approximate solutions to a nonintegrable problem of propagation of elliptically polarized waves in an isotropic gyrotropic nonlinear medium, and periodic analogues of multisoliton complexes,” Quantum Electron. 44(2), 130–134 (2014).
[Crossref]

V. A. Makarov, V. M. Petnikova, and V. V. Shuvalov, “Adiabatic approximation and aperiodic dynamics of an elliptically polarized light wave in an isotropic gyrotropic nonlinear medium,” Laser Phys. 24(8), 085405 (2014).
[Crossref]

V. M. Petnikova and V. V. Shuvalov, “Parametric frequency conversion, nonlinear Schrödinger equation, and multicomponent cnoidal waves,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046611 (2007).
[Crossref] [PubMed]

Potravkin, N. N.

V. A. Makarov, V. M. Petnikova, N. N. Potravkin, and V. V. Shuvalov, “Approximate solutions to a nonintegrable problem of propagation of elliptically polarized waves in an isotropic gyrotropic nonlinear medium, and periodic analogues of multisoliton complexes,” Quantum Electron. 44(2), 130–134 (2014).
[Crossref]

Redyuk, A. A.

O. V. Yushko and A. A. Redyuk, “Soliton communication lines based on spectrally efficient modulation formats,” Quantum Electron. 44(6), 606–611 (2014).
[Crossref]

Sahara, A.

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, “Recent progress in soliton transmission technology,” Chaos 10(3), 486–514 (2000).
[Crossref] [PubMed]

Segev, M.

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[Crossref] [PubMed]

Shuvalov, V. V.

V. A. Makarov, V. M. Petnikova, N. N. Potravkin, and V. V. Shuvalov, “Approximate solutions to a nonintegrable problem of propagation of elliptically polarized waves in an isotropic gyrotropic nonlinear medium, and periodic analogues of multisoliton complexes,” Quantum Electron. 44(2), 130–134 (2014).
[Crossref]

V. A. Makarov, V. M. Petnikova, and V. V. Shuvalov, “Adiabatic approximation and aperiodic dynamics of an elliptically polarized light wave in an isotropic gyrotropic nonlinear medium,” Laser Phys. 24(8), 085405 (2014).
[Crossref]

V. M. Petnikova and V. V. Shuvalov, “Parametric frequency conversion, nonlinear Schrödinger equation, and multicomponent cnoidal waves,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046611 (2007).
[Crossref] [PubMed]

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

Suzuki, K.

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, “Recent progress in soliton transmission technology,” Chaos 10(3), 486–514 (2000).
[Crossref] [PubMed]

Tang, X. Y.

X. P. Cheng, S. Y. Lou, C. L. Chen, and X. Y. Tang, “Interactions between solitons and other nonlinear Schrödinger waves,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 89(4), 043202 (2014).
[Crossref] [PubMed]

Umeton, C.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “All-optical switching and logic gating with spatial solitons in liquid crystals,” Appl. Phys. Lett. 81(18), 3335–3337 (2002).
[Crossref]

Wabnitz, S.

F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, and S. Wabnitz, “Vector rogue waves and baseband modulation instability in the defocusing regime,” Phys. Rev. Lett. 113(3), 034101 (2014).
[Crossref] [PubMed]

Wang, X. L.

B. G. Zhai, W. G. Zhang, X. L. Wang, and H. Q. Zhang, “Multi-rogue waves and rational solutions of the coupled nonlinear Schrödinger equations,” Nonlinear Anal. Real World Appl. 14(1), 14–27 (2013).
[Crossref]

Wen, S.

W. Cai, M. S. Mills, D. N. Christodoulides, and S. Wen, “Soliton manipulation using Airy pulses,” Opt. Commun. 316, 127–131 (2014).
[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, 463 (2012).
[Crossref] [PubMed]

Yamada, E.

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, “Recent progress in soliton transmission technology,” Chaos 10(3), 486–514 (2000).
[Crossref] [PubMed]

Yushko, O. V.

O. V. Yushko and A. A. Redyuk, “Soliton communication lines based on spectrally efficient modulation formats,” Quantum Electron. 44(6), 606–611 (2014).
[Crossref]

Zhai, B. G.

B. G. Zhai, W. G. Zhang, X. L. Wang, and H. Q. Zhang, “Multi-rogue waves and rational solutions of the coupled nonlinear Schrödinger equations,” Nonlinear Anal. Real World Appl. 14(1), 14–27 (2013).
[Crossref]

Zhang, H. Q.

B. G. Zhai, W. G. Zhang, X. L. Wang, and H. Q. Zhang, “Multi-rogue waves and rational solutions of the coupled nonlinear Schrödinger equations,” Nonlinear Anal. Real World Appl. 14(1), 14–27 (2013).
[Crossref]

Zhang, W. G.

B. G. Zhai, W. G. Zhang, X. L. Wang, and H. Q. Zhang, “Multi-rogue waves and rational solutions of the coupled nonlinear Schrödinger equations,” Nonlinear Anal. Real World Appl. 14(1), 14–27 (2013).
[Crossref]

Zhao, L. C.

L. C. Zhao and J. Liu, “Rogue-wave solutions of a three-component coupled nonlinear Schrödinger equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 87(1), 013201 (2013).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “All-optical switching and logic gating with spatial solitons in liquid crystals,” Appl. Phys. Lett. 81(18), 3335–3337 (2002).
[Crossref]

Chaos (1)

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, “Recent progress in soliton transmission technology,” Chaos 10(3), 486–514 (2000).
[Crossref] [PubMed]

Eur. Phys. J. Spec. Top. (1)

Yu. V. Bludov, V. V. Konotop, and N. Akhmediev, “Vector rogue waves in binary mixtures of Bose-Einstein condensates,” Eur. Phys. J. Spec. Top. 185(1), 169–180 (2010).
[Crossref]

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

C. Kalla, “Breathers and solitons of generalized nonlinear Schrödinger equations as degenerations of algebro-geometric solutions,” J. Phys. A: Math. Theor. 44(33), 335210 (2011).
[Crossref]

Laser Phys. (1)

V. A. Makarov, V. M. Petnikova, and V. V. Shuvalov, “Adiabatic approximation and aperiodic dynamics of an elliptically polarized light wave in an isotropic gyrotropic nonlinear medium,” Laser Phys. 24(8), 085405 (2014).
[Crossref]

Nat. Phys. (1)

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

Nature (1)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

Nonlinear Anal. Real World Appl. (1)

B. G. Zhai, W. G. Zhang, X. L. Wang, and H. Q. Zhang, “Multi-rogue waves and rational solutions of the coupled nonlinear Schrödinger equations,” Nonlinear Anal. Real World Appl. 14(1), 14–27 (2013).
[Crossref]

Opt. Commun. (1)

W. Cai, M. S. Mills, D. N. Christodoulides, and S. Wen, “Soliton manipulation using Airy pulses,” Opt. Commun. 316, 127–131 (2014).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (4)

V. M. Petnikova and V. V. Shuvalov, “Parametric frequency conversion, nonlinear Schrödinger equation, and multicomponent cnoidal waves,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046611 (2007).
[Crossref] [PubMed]

X. P. Cheng, S. Y. Lou, C. L. Chen, and X. Y. Tang, “Interactions between solitons and other nonlinear Schrödinger waves,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 89(4), 043202 (2014).
[Crossref] [PubMed]

X. R. Hu, S. Y. Lou, and Y. Chen, “Explicit solutions from eigenfunction symmetry of the Korteweg-de Vries equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(5), 056607 (2012).
[Crossref] [PubMed]

L. C. Zhao and J. Liu, “Rogue-wave solutions of a three-component coupled nonlinear Schrödinger equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 87(1), 013201 (2013).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, and S. Wabnitz, “Vector rogue waves and baseband modulation instability in the defocusing regime,” Phys. Rev. Lett. 113(3), 034101 (2014).
[Crossref] [PubMed]

Proc. R. Soc. Lond. A (1)

P. L. Christiansen, J. C. Eilbeck, V. Z. Enolskii, and N. A. Kostov, “Quasi-periodic and periodic solutions for Manakov type systems of coupled nonlinear Schrodinger equations,” Proc. R. Soc. Lond. A 456, 2263–2281 (2000).
[Crossref]

Quantum Electron. (2)

O. V. Yushko and A. A. Redyuk, “Soliton communication lines based on spectrally efficient modulation formats,” Quantum Electron. 44(6), 606–611 (2014).
[Crossref]

V. A. Makarov, V. M. Petnikova, N. N. Potravkin, and V. V. Shuvalov, “Approximate solutions to a nonintegrable problem of propagation of elliptically polarized waves in an isotropic gyrotropic nonlinear medium, and periodic analogues of multisoliton complexes,” Quantum Electron. 44(2), 130–134 (2014).
[Crossref]

Rep. Prog. Phys. (1)

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[Crossref] [PubMed]

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, 463 (2012).
[Crossref] [PubMed]

Other (6)

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 2007).

M. V. Berry, “Quantum, classical and semiclassical adiabaticity” in Theoretical and Applied Mechanics, F. I. Niordson and N. Olhoff, eds. (North-Holland Elsevier Science Publishers, 1985).

N. N. Akhmediev and A. Ankiewicz, Solitons, Nonlinear Pulses and Beams (Chapman & Hall, 1997).

B. A. Malomed, Soliton Management in Periodic Systems (Springer, 2006).

C. Kittel, Quantum Theory of Solids (Wiley, 1987).

K. P. Ho, Phase-Modulated Optical Communication Systems (Springer, 2005).

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Figures (2)

Fig. 1
Fig. 1 Dependencies of the rational soliton amplitude | A + ( z , t ) | (a) and of the cnoidal wave frequency ν ( z , t ) (b) for P 0 = 1 , ρ 0 = 1 , σ 1 = 1 , k 2 = 1 , κ = 1.5 , ρ 1 = 0.1 , σ 2 = 0.6 , μ = 0.7193 .
Fig. 2
Fig. 2 Dependencies r ( z , t ) (a) and r ( z , t ) (b) for odd and even cnoidal waves with the same parameters.

Equations (17)

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A + z i k 2 2 2 A + t 2 +i[ ρ 0 +( σ 1 /2 ρ 1 ) | A + | 2 +( σ 1 /2+ σ 2 ) | A | 2 ] A + =0,
A z i k 2 2 2 A t 2 +i[ + ρ 0 +( σ 1 /2+ ρ 1 ) | A | 2 +( σ 1 /2+ σ 2 ) | A + | 2 ] A =0.
A (z,t)= r (t)exp(i κ z),
d 2 r d t 2 2 k 2 [ Δ κ +( σ 1 2 + ρ 1 ) r 2 +( σ 1 2 + σ 2 ) | A + | 2 ] r =0.
A + z i k 2 2 2 A + t 2 +i[ ρ 0 +( σ 1 /2+ σ 2 ) r 2 t ] A + +i( σ 1 /2 ρ 1 ) | A + | 2 A + =0.
B 2 = 4 μ 2 Δ κ (2 μ 2 1)( σ 1 +2 ρ 1 ) [ 1+( σ 1 +2 σ 2 ) | A + | 2 /(2Δ κ ) ]>0, ν 2 = 2Δ κ k 2 (2 μ 2 1) [ 1+( σ 1 +2 σ 2 ) | A + | 2 /(2Δ κ ) ]>0.
r 2 t = 4Δ κ (2 μ 2 1)( σ 1 +2 ρ 1 ) [ μ 2 1+E( μ )/K( μ ) ][ 1+ ( σ 1 +2 σ 2 ) | A + | 2 2Δ κ ].
A + z i k 2 2 2 A + t 2 +i( ρ ^ 0 + d 2 | A + | 2 ) A + =0,
ρ ^ 0 = ρ 0 { 1+ 2Δ κ ( σ 1 +2 σ 2 ) ρ 0 (2 μ 2 1)( σ 1 +2 ρ 1 ) [ μ 2 1+E( μ )/K( μ ) ] },
d=( σ 1 2 ρ 1 ){ 1 2 ( σ 1 +2 σ 2 ) 2 (2 μ 2 1)( σ 1 2 4 ρ 1 2 ) [ μ 2 1+E( μ )/K( μ ) ] }.
A + (z,t)= P 0 ( 1 4(1iz P 0 d) 1+ (z P 0 d) 2 +2t P 2 0 d/| k 2 | )exp[ iz( ρ ^ 0 P 0 d/2 ) ], k 2 <0,
A (z,t)= r (z,t)exp(i κ z)= B (z,t)cn[ ν (z,t)t, μ ]exp(i κ z),
B 2 = B 2 (z,t)= 4 μ 2 Δ κ [1+m(z,t)] (2 μ 2 1)( σ 1 +2 ρ 1 ) >0, ν 2 = ν 2 (z,t)= 2Δ κ [1+m(z,t)] k 2 (2 μ 2 1) >0.
m(z,t)= ( σ 1 +2 σ 2 ) 2Δ κ | A + (z,t) | 2 = ( σ 1 +2 σ 2 ) P 0 2Δ κ ( 1+ 8[1+ (z P 0 d) 2 2t P 2 0 d/| k 2 |] [1+ (z P 0 d) 2 +2t P 2 0 d/| k 2 |] 2 ).
| σ 1 +2 σ 2 | P 0 <<0.3|Δ κ |.
( P 0 |d|) 1/2 <<|Δ κ | 1/2 /[4K( μ )|2 μ 2 1 | 1/2 ],
P 0 3/2 | σ 1 +2 σ 2 ||d | 1/2 <<2.5| κ ||Δ κ (2 μ 2 1) | 1/2 .

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