Abstract

We introduce three-dimensional (3D) spatiotemporal vector solitary waves in coupled (3+1)D nonlinear Schrödinger equations with variable diffraction and nonlinearity coefficients. The analysis is carried out in spherical coordinates, providing for novel localized solutions. Using the Hirota bilinear method, 3D approximate but analytical spatiotemporal vector solitary waves are built with the help of spherical harmonics, including multipole solutions and necklace rings. Variable diffraction and nonlinearity allow utilization of soliton management methods. The comparison with numerical solutions is provided and the behavior of relative error is displayed. It is demonstrated that the spatiotemporal soliton profiles found are stable in propagation.

© 2012 Optical Society of America

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  1. B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997).
    [CrossRef]
  2. H. He and P. D. Drummond, “Theory of multidimensional parametric band-gap simultons,” Phys. Rev. E 58, 5025–5046 (1998).
    [CrossRef]
  3. D. Mihalache, D. Mazilu, J. Dōrring, and L. Torner, “Elliptical light bullets,” Opt. Commun. 159, 129–138 (1999).
    [CrossRef]
  4. M. Blaauboer, B. A. Malomed, and G. Kurizki, “Temporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84, 1906–1909 (2000).
    [CrossRef]
  5. L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, “Tandem light bullets,” Opt. Commun. 199, 277–281 (2001).
    [CrossRef]
  6. P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
    [CrossRef]
  7. X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634(1999).
    [CrossRef]
  8. G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
    [CrossRef]
  9. X. Liu, K. Beckwitt, and F. W. Wise, “Noncollinear generation of optical spatiotemporal solitons and application to ultrafast digital logic,” Phys. Rev. E 61, R4722–R4725 (2000).
    [CrossRef]
  10. V. E. Lobanov, Y. V. Kartashov, and L. Torner, “Light bullets by synthetic diffraction-dispersion matching,” Phys. Rev. Lett. 105, 033901 (2010).
    [CrossRef]
  11. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
    [CrossRef]
  12. A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, and A. Naidenov, “Light bullets formation in a bulk media,” IEEE J. Quantum Electron. 27, 2060–2065 (1991).
    [CrossRef]
  13. W. P. Zhong and M. Belić, “Kummer solitons in strongly nonlocal nonlinear media,” Phys. Lett. A 373, 296–298 (2009).
    [CrossRef]
  14. I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, “Accessible light bullets via synergetic nonlinearities,” Phys. Rev. Lett. 102, 203903 (2009).
    [CrossRef]
  15. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
    [CrossRef]
  16. A. S. Desyatnikov and Yu. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87, 033901 (2001).
    [CrossRef]
  17. T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
    [CrossRef]
  18. D. Mihalache, D. Mazilu, F. Lederer, and Yu. S. Kivshar, “Interface discrete light bullets in waveguide arrays,” Opt. Lett. 32, 2091–2093 (2007).
    [CrossRef]
  19. L. Torner and Y. V. Kartashov, “Light bullets in optical tandems,” Opt. Lett. 34, 1129–1131 (2009).
    [CrossRef]
  20. W. P. Zhong, M. Belic, R. H. Xie, and G. Chen, “Two-dimensional Whittaker solitons in nonlocal nonlinear media,” Phys. Rev. A 78, 013826 (2008).
    [CrossRef]
  21. S. K. Adhikari, “Stabilization of bright solitons and vortex solitons in a trapless three-dimensional Bose–Einstein condensate by temporal modulation of the scattering length,” Phys. Rev. A 69, 063613 (2004).
    [CrossRef]
  22. S. K. Adhikari, “Stabilization of a light bullet in a layered Kerr medium with sign-changing nonlinearity,” Phys. Rev. E 70, 036608 (2004).
    [CrossRef]
  23. S. K. Adhikari, “Stabilization of a (3+1)D soliton in a Kerr medium by a rapidly oscillating dispersion coefficient,” Phys. Rev. E 71, 016611 (2005).
    [CrossRef]
  24. J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902 (2005).
    [CrossRef]
  25. D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice,” Phys. Rev. E 70, 055603R (2004).
    [CrossRef]
  26. D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
    [CrossRef]
  27. H. Leblond, B. A. Malomed, and D. Mihalache, “Three-dimensional vortex solitons in quasi-two-dimensional lattices,” Phys. Rev. E 76, 026604 (2007).
    [CrossRef]
  28. J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98, 064102 (2007).
    [CrossRef]
  29. J. He and Y. Li, “Designable integrability of the variable coefficient nonlinear Schrödinger equations,” Stud. Appl. Math. 126, 1–15 (2011).
    [CrossRef]
  30. W. Ping Zhong, M. Belić, G. Assanto, and T. Huang, “Three-dimensional spatiotemporal vector solitary waves,” J. Phys. B 44, 095403 (2011).
    [CrossRef]
  31. M. Belić, N. Petrović, W. P. Zhong, R. H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101, 123904 (2008).
    [CrossRef]
  32. W. P. Zhong, L. Yi, R. H. Xie, M. Belić, and G. Chen, “Robust three-dimensional spatial soliton clusters in strongly nonlocal media,” J. Phys. B 41, 025402 (2008).
    [CrossRef]
  33. R. Hirota, “Exact solution of the Korteweg–de Vries equation for multiple collisions of solitons,” Phys. Rev. Lett. 27, 1192–1194 (1971).
    [CrossRef]
  34. B. A. Malomed, Soliton Management in Periodic Systems (Springer, 2005).
  35. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose–Einstein condensation in trapped gases,” Rev. Mod. Phys. 71, 463–512 (1999).
    [CrossRef]

2011

J. He and Y. Li, “Designable integrability of the variable coefficient nonlinear Schrödinger equations,” Stud. Appl. Math. 126, 1–15 (2011).
[CrossRef]

W. Ping Zhong, M. Belić, G. Assanto, and T. Huang, “Three-dimensional spatiotemporal vector solitary waves,” J. Phys. B 44, 095403 (2011).
[CrossRef]

2010

V. E. Lobanov, Y. V. Kartashov, and L. Torner, “Light bullets by synthetic diffraction-dispersion matching,” Phys. Rev. Lett. 105, 033901 (2010).
[CrossRef]

2009

W. P. Zhong and M. Belić, “Kummer solitons in strongly nonlocal nonlinear media,” Phys. Lett. A 373, 296–298 (2009).
[CrossRef]

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, “Accessible light bullets via synergetic nonlinearities,” Phys. Rev. Lett. 102, 203903 (2009).
[CrossRef]

L. Torner and Y. V. Kartashov, “Light bullets in optical tandems,” Opt. Lett. 34, 1129–1131 (2009).
[CrossRef]

2008

M. Belić, N. Petrović, W. P. Zhong, R. H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101, 123904 (2008).
[CrossRef]

W. P. Zhong, L. Yi, R. H. Xie, M. Belić, and G. Chen, “Robust three-dimensional spatial soliton clusters in strongly nonlocal media,” J. Phys. B 41, 025402 (2008).
[CrossRef]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

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

2007

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

H. Leblond, B. A. Malomed, and D. Mihalache, “Three-dimensional vortex solitons in quasi-two-dimensional lattices,” Phys. Rev. E 76, 026604 (2007).
[CrossRef]

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, and Yu. S. Kivshar, “Interface discrete light bullets in waveguide arrays,” Opt. Lett. 32, 2091–2093 (2007).
[CrossRef]

2005

S. K. Adhikari, “Stabilization of a (3+1)D soliton in a Kerr medium by a rapidly oscillating dispersion coefficient,” Phys. Rev. E 71, 016611 (2005).
[CrossRef]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef]

2004

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice,” Phys. Rev. E 70, 055603R (2004).
[CrossRef]

S. K. Adhikari, “Stabilization of bright solitons and vortex solitons in a trapless three-dimensional Bose–Einstein condensate by temporal modulation of the scattering length,” Phys. Rev. A 69, 063613 (2004).
[CrossRef]

S. K. Adhikari, “Stabilization of a light bullet in a layered Kerr medium with sign-changing nonlinearity,” Phys. Rev. E 70, 036608 (2004).
[CrossRef]

2003

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

2002

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

2001

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, “Tandem light bullets,” Opt. Commun. 199, 277–281 (2001).
[CrossRef]

A. S. Desyatnikov and Yu. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87, 033901 (2001).
[CrossRef]

2000

X. Liu, K. Beckwitt, and F. W. Wise, “Noncollinear generation of optical spatiotemporal solitons and application to ultrafast digital logic,” Phys. Rev. E 61, R4722–R4725 (2000).
[CrossRef]

M. Blaauboer, B. A. Malomed, and G. Kurizki, “Temporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84, 1906–1909 (2000).
[CrossRef]

1999

D. Mihalache, D. Mazilu, J. Dōrring, and L. Torner, “Elliptical light bullets,” Opt. Commun. 159, 129–138 (1999).
[CrossRef]

X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634(1999).
[CrossRef]

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
[CrossRef]

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose–Einstein condensation in trapped gases,” Rev. Mod. Phys. 71, 463–512 (1999).
[CrossRef]

1998

H. He and P. D. Drummond, “Theory of multidimensional parametric band-gap simultons,” Phys. Rev. E 58, 5025–5046 (1998).
[CrossRef]

1997

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997).
[CrossRef]

1991

A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, and A. Naidenov, “Light bullets formation in a bulk media,” IEEE J. Quantum Electron. 27, 2060–2065 (1991).
[CrossRef]

1971

R. Hirota, “Exact solution of the Korteweg–de Vries equation for multiple collisions of solitons,” Phys. Rev. Lett. 27, 1192–1194 (1971).
[CrossRef]

Adhikari, S. K.

S. K. Adhikari, “Stabilization of a (3+1)D soliton in a Kerr medium by a rapidly oscillating dispersion coefficient,” Phys. Rev. E 71, 016611 (2005).
[CrossRef]

S. K. Adhikari, “Stabilization of bright solitons and vortex solitons in a trapless three-dimensional Bose–Einstein condensate by temporal modulation of the scattering length,” Phys. Rev. A 69, 063613 (2004).
[CrossRef]

S. K. Adhikari, “Stabilization of a light bullet in a layered Kerr medium with sign-changing nonlinearity,” Phys. Rev. E 70, 036608 (2004).
[CrossRef]

Anderson, D.

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997).
[CrossRef]

Assanto, G.

W. Ping Zhong, M. Belić, G. Assanto, and T. Huang, “Three-dimensional spatiotemporal vector solitary waves,” J. Phys. B 44, 095403 (2011).
[CrossRef]

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, “Accessible light bullets via synergetic nonlinearities,” Phys. Rev. Lett. 102, 203903 (2009).
[CrossRef]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

Beckwitt, K.

X. Liu, K. Beckwitt, and F. W. Wise, “Noncollinear generation of optical spatiotemporal solitons and application to ultrafast digital logic,” Phys. Rev. E 61, R4722–R4725 (2000).
[CrossRef]

Belic, M.

W. Ping Zhong, M. Belić, G. Assanto, and T. Huang, “Three-dimensional spatiotemporal vector solitary waves,” J. Phys. B 44, 095403 (2011).
[CrossRef]

W. P. Zhong and M. Belić, “Kummer solitons in strongly nonlocal nonlinear media,” Phys. Lett. A 373, 296–298 (2009).
[CrossRef]

W. P. Zhong, L. Yi, R. H. Xie, M. Belić, and G. Chen, “Robust three-dimensional spatial soliton clusters in strongly nonlocal media,” J. Phys. B 41, 025402 (2008).
[CrossRef]

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

M. Belić, N. Petrović, W. P. Zhong, R. H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101, 123904 (2008).
[CrossRef]

Belmonte-Beitia, J.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef]

Bergé, L.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Berntson, A.

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997).
[CrossRef]

Blaauboer, M.

M. Blaauboer, B. A. Malomed, and G. Kurizki, “Temporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84, 1906–1909 (2000).
[CrossRef]

Blagoeva, A. B.

A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, and A. Naidenov, “Light bullets formation in a bulk media,” IEEE J. Quantum Electron. 27, 2060–2065 (1991).
[CrossRef]

Bräuer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Burgess, I. B.

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, “Accessible light bullets via synergetic nonlinearities,” Phys. Rev. Lett. 102, 203903 (2009).
[CrossRef]

Carrasco, S.

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, “Tandem light bullets,” Opt. Commun. 199, 277–281 (2001).
[CrossRef]

Chen, G.

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

M. Belić, N. Petrović, W. P. Zhong, R. H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101, 123904 (2008).
[CrossRef]

W. P. Zhong, L. Yi, R. H. Xie, M. Belić, and G. Chen, “Robust three-dimensional spatial soliton clusters in strongly nonlocal media,” J. Phys. B 41, 025402 (2008).
[CrossRef]

Chen, Z.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef]

Christodoulides, D. N.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

Conti, C.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Crasovan, L. C.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice,” Phys. Rev. E 70, 055603R (2004).
[CrossRef]

Crasovan, L.-C.

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, “Tandem light bullets,” Opt. Commun. 199, 277–281 (2001).
[CrossRef]

Dalfovo, F.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose–Einstein condensation in trapped gases,” Rev. Mod. Phys. 71, 463–512 (1999).
[CrossRef]

Desyatnikov, A. S.

A. S. Desyatnikov and Yu. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87, 033901 (2001).
[CrossRef]

Di Trapani, P.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Dinev, S. G.

A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, and A. Naidenov, “Light bullets formation in a bulk media,” IEEE J. Quantum Electron. 27, 2060–2065 (1991).
[CrossRef]

Dorring, J.

D. Mihalache, D. Mazilu, J. Dōrring, and L. Torner, “Elliptical light bullets,” Opt. Commun. 159, 129–138 (1999).
[CrossRef]

Dreischuh, A. A.

A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, and A. Naidenov, “Light bullets formation in a bulk media,” IEEE J. Quantum Electron. 27, 2060–2065 (1991).
[CrossRef]

Drummond, P.

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997).
[CrossRef]

Drummond, P. D.

H. He and P. D. Drummond, “Theory of multidimensional parametric band-gap simultons,” Phys. Rev. E 58, 5025–5046 (1998).
[CrossRef]

Frantzeskakis, D. J.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef]

Giorgini, S.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose–Einstein condensation in trapped gases,” Rev. Mod. Phys. 71, 463–512 (1999).
[CrossRef]

He, H.

H. He and P. D. Drummond, “Theory of multidimensional parametric band-gap simultons,” Phys. Rev. E 58, 5025–5046 (1998).
[CrossRef]

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997).
[CrossRef]

He, J.

J. He and Y. Li, “Designable integrability of the variable coefficient nonlinear Schrödinger equations,” Stud. Appl. Math. 126, 1–15 (2011).
[CrossRef]

Hirota, R.

R. Hirota, “Exact solution of the Korteweg–de Vries equation for multiple collisions of solitons,” Phys. Rev. Lett. 27, 1192–1194 (1971).
[CrossRef]

Huang, T.

W. Ping Zhong, M. Belić, G. Assanto, and T. Huang, “Three-dimensional spatiotemporal vector solitary waves,” J. Phys. B 44, 095403 (2011).
[CrossRef]

Jedrkiewicz, O.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Kartashov, Y. V.

V. E. Lobanov, Y. V. Kartashov, and L. Torner, “Light bullets by synthetic diffraction-dispersion matching,” Phys. Rev. Lett. 105, 033901 (2010).
[CrossRef]

L. Torner and Y. V. Kartashov, “Light bullets in optical tandems,” Opt. Lett. 34, 1129–1131 (2009).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice,” Phys. Rev. E 70, 055603R (2004).
[CrossRef]

Kasparian, J.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Kevrekidis, P. G.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef]

Kivshar, Yu. S.

Kurizki, G.

M. Blaauboer, B. A. Malomed, and G. Kurizki, “Temporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84, 1906–1909 (2000).
[CrossRef]

Leblond, H.

H. Leblond, B. A. Malomed, and D. Mihalache, “Three-dimensional vortex solitons in quasi-two-dimensional lattices,” Phys. Rev. E 76, 026604 (2007).
[CrossRef]

Lederer, F.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, and Yu. S. Kivshar, “Interface discrete light bullets in waveguide arrays,” Opt. Lett. 32, 2091–2093 (2007).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice,” Phys. Rev. E 70, 055603R (2004).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Li, Y.

J. He and Y. Li, “Designable integrability of the variable coefficient nonlinear Schrödinger equations,” Stud. Appl. Math. 126, 1–15 (2011).
[CrossRef]

Lisak, M.

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997).
[CrossRef]

Liu, X.

X. Liu, K. Beckwitt, and F. W. Wise, “Noncollinear generation of optical spatiotemporal solitons and application to ultrafast digital logic,” Phys. Rev. E 61, R4722–R4725 (2000).
[CrossRef]

X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634(1999).
[CrossRef]

Lobanov, V. E.

V. E. Lobanov, Y. V. Kartashov, and L. Torner, “Light bullets by synthetic diffraction-dispersion matching,” Phys. Rev. Lett. 105, 033901 (2010).
[CrossRef]

Makasyuk, I.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef]

Malomed, B. A.

H. Leblond, B. A. Malomed, and D. Mihalache, “Three-dimensional vortex solitons in quasi-two-dimensional lattices,” Phys. Rev. E 76, 026604 (2007).
[CrossRef]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef]

M. Blaauboer, B. A. Malomed, and G. Kurizki, “Temporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84, 1906–1909 (2000).
[CrossRef]

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997).
[CrossRef]

B. A. Malomed, Soliton Management in Periodic Systems (Springer, 2005).

Martin, H.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef]

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, and Yu. S. Kivshar, “Interface discrete light bullets in waveguide arrays,” Opt. Lett. 32, 2091–2093 (2007).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice,” Phys. Rev. E 70, 055603R (2004).
[CrossRef]

D. Mihalache, D. Mazilu, J. Dōrring, and L. Torner, “Elliptical light bullets,” Opt. Commun. 159, 129–138 (1999).
[CrossRef]

Mihalache, D.

D. Mihalache, D. Mazilu, F. Lederer, and Yu. S. Kivshar, “Interface discrete light bullets in waveguide arrays,” Opt. Lett. 32, 2091–2093 (2007).
[CrossRef]

H. Leblond, B. A. Malomed, and D. Mihalache, “Three-dimensional vortex solitons in quasi-two-dimensional lattices,” Phys. Rev. E 76, 026604 (2007).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice,” Phys. Rev. E 70, 055603R (2004).
[CrossRef]

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, “Tandem light bullets,” Opt. Commun. 199, 277–281 (2001).
[CrossRef]

D. Mihalache, D. Mazilu, J. Dōrring, and L. Torner, “Elliptical light bullets,” Opt. Commun. 159, 129–138 (1999).
[CrossRef]

Morandotti, R.

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, “Accessible light bullets via synergetic nonlinearities,” Phys. Rev. Lett. 102, 203903 (2009).
[CrossRef]

Naidenov, A.

A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, and A. Naidenov, “Light bullets formation in a bulk media,” IEEE J. Quantum Electron. 27, 2060–2065 (1991).
[CrossRef]

Nuter, R.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Peccianti, M.

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, “Accessible light bullets via synergetic nonlinearities,” Phys. Rev. Lett. 102, 203903 (2009).
[CrossRef]

Perez-Garcia, V. M.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef]

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Peschel, U.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Petrovic, N.

M. Belić, N. Petrović, W. P. Zhong, R. H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101, 123904 (2008).
[CrossRef]

Piskarskas, A.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Pitaevskii, L. P.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose–Einstein condensation in trapped gases,” Rev. Mod. Phys. 71, 463–512 (1999).
[CrossRef]

Qian, L. J.

X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634(1999).
[CrossRef]

Segev, M.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
[CrossRef]

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

Skupin, S.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
[CrossRef]

Stringari, S.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose–Einstein condensation in trapped gases,” Rev. Mod. Phys. 71, 463–512 (1999).
[CrossRef]

Torner, L.

V. E. Lobanov, Y. V. Kartashov, and L. Torner, “Light bullets by synthetic diffraction-dispersion matching,” Phys. Rev. Lett. 105, 033901 (2010).
[CrossRef]

L. Torner and Y. V. Kartashov, “Light bullets in optical tandems,” Opt. Lett. 34, 1129–1131 (2009).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice,” Phys. Rev. E 70, 055603R (2004).
[CrossRef]

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, “Tandem light bullets,” Opt. Commun. 199, 277–281 (2001).
[CrossRef]

D. Mihalache, D. Mazilu, J. Dōrring, and L. Torner, “Elliptical light bullets,” Opt. Commun. 159, 129–138 (1999).
[CrossRef]

Torres, J. P.

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, “Tandem light bullets,” Opt. Commun. 199, 277–281 (2001).
[CrossRef]

Torres, P. J.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef]

Trillo, S.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Trull, J.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Valiulis, G.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Vekslerchik, V.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef]

Wise, F. W.

X. Liu, K. Beckwitt, and F. W. Wise, “Noncollinear generation of optical spatiotemporal solitons and application to ultrafast digital logic,” Phys. Rev. E 61, R4722–R4725 (2000).
[CrossRef]

X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634(1999).
[CrossRef]

Wolf, J. P.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Xie, R. H.

W. P. Zhong, L. Yi, R. H. Xie, M. Belić, and G. Chen, “Robust three-dimensional spatial soliton clusters in strongly nonlocal media,” J. Phys. B 41, 025402 (2008).
[CrossRef]

M. Belić, N. Petrović, W. P. Zhong, R. H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101, 123904 (2008).
[CrossRef]

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

Yang, J.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef]

Yi, L.

W. P. Zhong, L. Yi, R. H. Xie, M. Belić, and G. Chen, “Robust three-dimensional spatial soliton clusters in strongly nonlocal media,” J. Phys. B 41, 025402 (2008).
[CrossRef]

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Zhong, W. P.

W. P. Zhong and M. Belić, “Kummer solitons in strongly nonlocal nonlinear media,” Phys. Lett. A 373, 296–298 (2009).
[CrossRef]

W. P. Zhong, L. Yi, R. H. Xie, M. Belić, and G. Chen, “Robust three-dimensional spatial soliton clusters in strongly nonlocal media,” J. Phys. B 41, 025402 (2008).
[CrossRef]

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

M. Belić, N. Petrović, W. P. Zhong, R. H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101, 123904 (2008).
[CrossRef]

Zhong, W. Ping

W. Ping Zhong, M. Belić, G. Assanto, and T. Huang, “Three-dimensional spatiotemporal vector solitary waves,” J. Phys. B 44, 095403 (2011).
[CrossRef]

IEEE J. Quantum Electron.

A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, and A. Naidenov, “Light bullets formation in a bulk media,” IEEE J. Quantum Electron. 27, 2060–2065 (1991).
[CrossRef]

J. Phys. B

W. Ping Zhong, M. Belić, G. Assanto, and T. Huang, “Three-dimensional spatiotemporal vector solitary waves,” J. Phys. B 44, 095403 (2011).
[CrossRef]

W. P. Zhong, L. Yi, R. H. Xie, M. Belić, and G. Chen, “Robust three-dimensional spatial soliton clusters in strongly nonlocal media,” J. Phys. B 41, 025402 (2008).
[CrossRef]

Opt. Commun.

D. Mihalache, D. Mazilu, J. Dōrring, and L. Torner, “Elliptical light bullets,” Opt. Commun. 159, 129–138 (1999).
[CrossRef]

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, “Tandem light bullets,” Opt. Commun. 199, 277–281 (2001).
[CrossRef]

Opt. Lett.

Phys. Lett. A

W. P. Zhong and M. Belić, “Kummer solitons in strongly nonlocal nonlinear media,” Phys. Lett. A 373, 296–298 (2009).
[CrossRef]

Phys. Rep.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

Phys. Rev. A

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

S. K. Adhikari, “Stabilization of bright solitons and vortex solitons in a trapless three-dimensional Bose–Einstein condensate by temporal modulation of the scattering length,” Phys. Rev. A 69, 063613 (2004).
[CrossRef]

Phys. Rev. E

S. K. Adhikari, “Stabilization of a light bullet in a layered Kerr medium with sign-changing nonlinearity,” Phys. Rev. E 70, 036608 (2004).
[CrossRef]

S. K. Adhikari, “Stabilization of a (3+1)D soliton in a Kerr medium by a rapidly oscillating dispersion coefficient,” Phys. Rev. E 71, 016611 (2005).
[CrossRef]

X. Liu, K. Beckwitt, and F. W. Wise, “Noncollinear generation of optical spatiotemporal solitons and application to ultrafast digital logic,” Phys. Rev. E 61, R4722–R4725 (2000).
[CrossRef]

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997).
[CrossRef]

H. He and P. D. Drummond, “Theory of multidimensional parametric band-gap simultons,” Phys. Rev. E 58, 5025–5046 (1998).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice,” Phys. Rev. E 70, 055603R (2004).
[CrossRef]

H. Leblond, B. A. Malomed, and D. Mihalache, “Three-dimensional vortex solitons in quasi-two-dimensional lattices,” Phys. Rev. E 76, 026604 (2007).
[CrossRef]

Phys. Rev. Lett.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef]

M. Belić, N. Petrović, W. P. Zhong, R. H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101, 123904 (2008).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L. C. Crasovan, and L. Torner, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef]

A. S. Desyatnikov and Yu. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87, 033901 (2001).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

R. Hirota, “Exact solution of the Korteweg–de Vries equation for multiple collisions of solitons,” Phys. Rev. Lett. 27, 1192–1194 (1971).
[CrossRef]

M. Blaauboer, B. A. Malomed, and G. Kurizki, “Temporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84, 1906–1909 (2000).
[CrossRef]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634(1999).
[CrossRef]

V. E. Lobanov, Y. V. Kartashov, and L. Torner, “Light bullets by synthetic diffraction-dispersion matching,” Phys. Rev. Lett. 105, 033901 (2010).
[CrossRef]

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, “Accessible light bullets via synergetic nonlinearities,” Phys. Rev. Lett. 102, 203903 (2009).
[CrossRef]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef]

Rep. Prog. Phys.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Rev. Mod. Phys.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose–Einstein condensation in trapped gases,” Rev. Mod. Phys. 71, 463–512 (1999).
[CrossRef]

Science

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
[CrossRef]

Stud. Appl. Math.

J. He and Y. Li, “Designable integrability of the variable coefficient nonlinear Schrödinger equations,” Stud. Appl. Math. 126, 1–15 (2011).
[CrossRef]

Other

B. A. Malomed, Soliton Management in Periodic Systems (Springer, 2005).

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Figures (10)

Fig. 1.
Fig. 1.

Intensity distributions of 3D LBs with m=0 and different l (l=0,1,2) from left to right. The coefficient functions are β(z)=β0cos(z), χ(z)=χ0cos(z); other parameters are z=2, a10=β0=χ0=1, c1=4, D1=3.

Fig. 2.
Fig. 2.

Dynamics of 3D vector LBs with l=m and q=0 at z=1. l=m=1,2,3 from top to bottom; the other parameters are as in Fig. 1.

Fig. 3.
Fig. 3.

Examples of vortex LBs with lm and q=0 at z=1. l=3, m=2,1 from top to bottom; the other parameters are as in Fig. 1.

Fig. 4.
Fig. 4.

Intensity distribution of 3D vector LBs in the x-y plane at z=2 with q=0, τ=1, l=3, and m=1,2,3 from top to bottom; the other parameters are as in Fig. 1.

Fig. 5.
Fig. 5.

Intensity distribution of 3D vector LBs in x-y plane with l=2, m=1, and q=0.2,0.8,1 from top to bottom; the other parameters are as in Fig. 4.

Fig. 6.
Fig. 6.

(a), (c) Evolution of the radial field distribution |V|2; (b), (d) corresponding intensity contour plots in the rz planes. Here l=2 in (a) and (b), and l=0 in (c) and (d). Other parameters are as in Fig. 1.

Fig. 7.
Fig. 7.

Evolution of the first-order solitary waves. (a), (b) Intensity contour plots in the x/yz planes, and (b), (d) in the τz plane. The corresponding parameters are l=2, m=1, q=0, y/x=τ=1 [(a), (b)], x=y=1 [(c), (d)]. Other parameters are as in Fig. 1.

Fig. 8.
Fig. 8.

Evolution of the first-order 3D vector LB at z=1. (a)–(c) Intensity contour plots in the x-y plane. (d)–(f) Corresponding phase distributions. The corresponding parameters are l=m=3, q=0.6; the other parameters are as in Fig. 4.

Fig. 9.
Fig. 9.

Comparison of the simulated LBs with analytical predictions. (a)–(c) and (d)–(f) display the simulated chirp and intensity (solid curves) together with the analytical predictions (dashed curves), with l=m=3, q=0.6; (g)–(i) display the percent relative error of amplitude for different m=0,1,2 (from left to right). The other parameters are as in Fig. 4.

Fig. 10.
Fig. 10.

Comparison of isosurfaces of LBs of analytical solutions with the numerical simulations of Eq. (1) for various distances z=8, 12, 16, from left to right. Analytical solution (top row); numerical simulation (middle row); numerical simulation with a white noise of variance σ=0.08 added to the input (bottom row). The corresponding parameters are l=m=2, q=0, and the other parameters are as in Fig. 1.

Equations (21)

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iunz+β(z)22un+χ(z)F(I)un=0,
un(z,r,θ,φ)=V(z,r)Yn(θ,φ),
Yn[iVz+β(z)rVr+β(z)22Vr2+χ(z)n=1N|Yn|2|V|2V]+β(z)V2r2[1sinθθ(sinθθ)Yn+1sin2θ2Ynφ2]=0.
1Yn[1sinθθ(sinθθ)Yn+1sin2θ2Ynφ2]=l(l+1),
2r2β(z)V[iVz+β(z)rVr+β(z)22Vr2+χ(z)|V|2V]=l(l+1).
n=1N|An|2=n=1N|Bn|2=1,
n=1NRe(AnBn*)=0.
A1=(1+q2)1/2,B1=iqA1,
A2=qA1,B2=±iA1,
iVz+12β(z)(2r2+2rr)V+χ(z)|V|2Vl(l+1)2r2β(z)V=0.
H1[gf]=0,
H2[ff]=2χ(z)β(z)r2lgg*,
g(r,z)=εg1(r,z)+ε3g3(r,z)++ε2j+1g2j+1(r,z)+,f(r,z)=1+ε2f2(r,z)+ε4f4(r,z)++ε2jf2j(r,z)+.
ε1:H1[g11]=0,
ε2:H2[1f2+f21]=2χ(z)β(z)r2lg1g1*,
ε3:H1[g1f2+g31]=0,
ε4:H2[1f4+f41+f2f2]=2χ(z)β(z)r2l(g1g3*+g3g1*).
g1=a10(c12iβ(z)dz)2l+32exp{r2c12iβ(z)dz+D1},
anddf22dr2=χ(z)β(z)r2lg1g1*,
Vl(r,z)=rlg11+f2.
unlm(z,r,θ,φ)=Kϕnm(φ)Plm(cosθ)g11+f2rl.

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