Abstract

We analyze three-dimensional (3D) vector solitary waves in a system of coupled nonlinear Schrödinger equations with spatially modulated diffraction and nonlinearity, under action of a composite self-consistent trapping potential. Exact vector solitary waves, or light bullets (LBs), are found using the self-similarity method. The stability of vortex 3D LB pairs is examined by direct numerical simulations; the results show that only low-order vortex soliton pairs with the mode parameter values n ≤ 1, l ≤ 1 and m = 0 can be supported by the spatially modulated interaction in the composite trap. Higher-order LBs are found unstable over prolonged distances.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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2016 (3)

B. Malomed, L. Torner, F. Wise, and D. Mihalache, “On multidimensional solitons and their legacy in contemporary Atomic, Molecular and Optical physics,” J. Phys. At. Mol. Opt. Phys. 49(17), 170502 (2016).
[Crossref]

S. L. Xu, J. X. Cheng, M. R. Belić, Z. L. Hu, and Y. Zhao, “Dynamics of nonlinear waves in two-dimensional cubic-quintic nonlinear Schrödinger equation with spatially modulated nonlinearities and potentials,” Opt. Express 24(9), 10066–10077 (2016).
[Crossref] [PubMed]

S. L. Xu, N. Z. Petrovic, M. R. Belić, and W. W. Deng, “Exact solutions for the quintic nonlinear Schrödinger equation with time and space,” Nonlinear Dyn. 84(1), 251–259 (2016).
[Crossref]

2015 (4)

S. L. Xu and M. R. Belic, “Light bullets in coupled nonlinear Schrödinger equation with spatially modulated coefficients and Bessel trapping potential,” J. Mod. Opt. 62(9), 683–692 (2015).
[Crossref]

A. I. Yakimenko, S. I. Vilchinskii, Y. M. Bidasyuk, Y. I. Kuriatnikov, K. O. Isaieva, and M. Weyrauch, “Generation and decay of persistent currents in a toroidal Bose-Einstein condensate,” Rom. Rep. Phys. 67, 249–272 (2015).

S. L. Xu, G. P. Zhou, N. Z. Petrović, and M. R. Belić, “Nonautonomous vector matter waves in two-component Bose-Einstein condensates with combined time-dependent harmonic-lattice potential,” J. Opt. 17(10), 105605 (2015).
[Crossref]

V. S. Bagnato, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and D. Mihalache, “Bose-Einstein condensation: Twenty years after,” Rom. Rep. Phys. 67, 5–50 (2015).

2014 (1)

D. J. Frantzeskakis, H. Leblond, and D. Mihalache, “Nonlinear optics of intense few-cycle pulses: An overview of recent theoretical and experimental developments,” Rom. J. Phys. 59, 767–784 (2014).

2013 (4)

W.-P. Zhong and M. Belic, “Resonance solitons produced by azimuthal modulation in self-focusing and self-defocusing materials,” Nonlinear Dyn. 73(4), 2091–2102 (2013).
[Crossref]

T. X. Tran and F. Biancalana, “Diffractive resonant radiation emitted by spatial solitons in waveguide arrays,” Phys. Rev. Lett. 110(11), 113903 (2013).
[Crossref] [PubMed]

A. I. Yakimenko, K. O. Isaieva, S. I. Vilchinskii, and M. Weyrauch, “Stability of persistent currents in spinor Bose-Einstein condensates,” Phys. Rev. A 88(5), 051602 (2013).
[Crossref]

S. L. Xu, M. R. Belić, and W. P. Zhong, “Three-dimensional spatio-temporal vector solitary waves in coupled nonlinear Schrödinger equations with variable coefficients,” J. Opt. Soc. Am. B 30(1), 113–122 (2013).
[Crossref]

2012 (1)

S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in PT-symmetric optical lattices,” Phys. Rev. A 85(2), 023822 (2012).
[Crossref]

2011 (2)

W. P. Zhong, M. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Self-trapping of scalar and vector dipole solitary waves in Kerr media,” Phys. Rev. A 83(4), 043833 (2011).
[Crossref]

D. S. Wang, S. W. Song, B. Xiong, and W. M. Liu, “Quantized vortices in a rotating Bose-Einstein condensate with spatiotemporally modulated interaction,” Phys. Rev. A 84(5), 053607 (2011).
[Crossref]

2010 (1)

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

2009 (3)

A. T. Avelar, D. Bazeia, and W. B. Cardoso, “Solitons with cubic and quintic nonlinearities modulated in space and time,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 025602 (2009).
[Crossref] [PubMed]

A. I. Yakimenko, Y. A. Zaliznyak, and V. M. Lashkin, “Two-dimensional nonlinear vector states in Bose-Einstein condensates,” Phys. Rev. A 79(4), 043629 (2009).
[Crossref]

A. V. Gorbach and D. V. Skryabin, “Spatial solitons in periodic nanostructures,” Phys. Rev. A 79(5), 053812 (2009).
[Crossref]

2008 (3)

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78(3), 031801 (2008).
[Crossref]

K. Gallo, A. Pasquazi, S. Stivala, and G. Assanto, “Parametric solitons in two-dimensional lattices of purely nonlinear origin,” Phys. Rev. Lett. 100(5), 053901 (2008).
[Crossref] [PubMed]

M. Dehghan and D. Mirzaei, “The dual reciprocity boundary element method (DRBEM) for two-dimensional sine-Gordon equation,” Comput. Methods Appl. Mech. Eng. 197(6-8), 476–486 (2008).
[Crossref]

2005 (2)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B Quantum Semiclassical Opt. 7(5), R53–R72 (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(2), 023902 (2005).
[Crossref] [PubMed]

2004 (2)

Y. F. Chen, K. Beckwitt, F. W. Wise, and B. A. Malomed, “Criteria for the experimental observation of multidimensional optical solitons in saturable media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046610 (2004).
[Crossref] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in bessel optical lattices,” Phys. Rev. Lett. 93(9), 093904 (2004).
[Crossref] [PubMed]

2003 (2)

L. C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, “Soliton “molecules”: robust clusters of spatiotemporal optical solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046610 (2003).
[Crossref] [PubMed]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
[Crossref] [PubMed]

2002 (3)

D. Mihalache, D. Mazilu, L. C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref] [PubMed]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046619 (2002).
[Crossref] [PubMed]

C. Weilnau, M. Ahles, J. Petter, D. Träger, J. Schröder, and C. Denz, “Spatial optical (2+1)-dimensional scalar- and vector solitons in saturable nonlinear media,” Ann. Phys. 11(8), 573–629 (2002).
[Crossref]

2001 (2)

A. S. Desyatnikov and Y. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87(3), 033901 (2001).
[Crossref] [PubMed]

W. Królikowski and O. Bang, “Solitons in nonlocal nonlinear media: exact solutions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(1 Pt 2), 016610 (2001).
[PubMed]

2000 (1)

M. Blaauboer, B. A. Malomed, and G. Kurizki, “Spatiotemporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84(9), 1906–1909 (2000).
[Crossref] [PubMed]

1999 (1)

X. Liu, K. Beckwitt, and F. Wise, “Generation of optical spatiotemporal solitons,” Opt. Photonics News 82, 4631–4634 (1999).

1998 (2)

L. Bergé, “Wave collapse in physics: principles and applications to light and plasma waves,” Phys. Rep. 303(5-6), 259–370 (1998).
[Crossref]

L. Bergé, “Wave collapse in physics: principles and applications to light and plasma waves,” Phys. Rep. 303(5-6), 259–370 (1998).
[Crossref]

1995 (1)

D. E. Edmundson and R. H. Enns, “Particlelike nature of colliding three-dimensional optical solitons,” Phys. Rev. A 51(3), 2491–2498 (1995).
[Crossref] [PubMed]

1990 (1)

1974 (1)

S. V. Manakov, “Theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974).

1971 (1)

R. Hirota, “Exact Solution of the Korteweg-de Vries Equation for Multiple Collisions of Solitons,” Phys. Rev. Lett. 27(18), 1192–1194 (1971).
[Crossref]

Abdollahpour, D.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

Ahles, M.

C. Weilnau, M. Ahles, J. Petter, D. Träger, J. Schröder, and C. Denz, “Spatial optical (2+1)-dimensional scalar- and vector solitons in saturable nonlinear media,” Ann. Phys. 11(8), 573–629 (2002).
[Crossref]

Assanto, G.

W. P. Zhong, M. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Self-trapping of scalar and vector dipole solitary waves in Kerr media,” Phys. Rev. A 83(4), 043833 (2011).
[Crossref]

K. Gallo, A. Pasquazi, S. Stivala, and G. Assanto, “Parametric solitons in two-dimensional lattices of purely nonlinear origin,” Phys. Rev. Lett. 100(5), 053901 (2008).
[Crossref] [PubMed]

Avelar, A. T.

A. T. Avelar, D. Bazeia, and W. B. Cardoso, “Solitons with cubic and quintic nonlinearities modulated in space and time,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 025602 (2009).
[Crossref] [PubMed]

Bagnato, V. S.

V. S. Bagnato, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and D. Mihalache, “Bose-Einstein condensation: Twenty years after,” Rom. Rep. Phys. 67, 5–50 (2015).

Bang, O.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046619 (2002).
[Crossref] [PubMed]

W. Królikowski and O. Bang, “Solitons in nonlocal nonlinear media: exact solutions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(1 Pt 2), 016610 (2001).
[PubMed]

Bazeia, D.

A. T. Avelar, D. Bazeia, and W. B. Cardoso, “Solitons with cubic and quintic nonlinearities modulated in space and time,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 025602 (2009).
[Crossref] [PubMed]

Beckwitt, K.

Y. F. Chen, K. Beckwitt, F. W. Wise, and B. A. Malomed, “Criteria for the experimental observation of multidimensional optical solitons in saturable media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046610 (2004).
[Crossref] [PubMed]

X. Liu, K. Beckwitt, and F. Wise, “Generation of optical spatiotemporal solitons,” Opt. Photonics News 82, 4631–4634 (1999).

Belic, M.

W.-P. Zhong and M. Belic, “Resonance solitons produced by azimuthal modulation in self-focusing and self-defocusing materials,” Nonlinear Dyn. 73(4), 2091–2102 (2013).
[Crossref]

W. P. Zhong, M. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Self-trapping of scalar and vector dipole solitary waves in Kerr media,” Phys. Rev. A 83(4), 043833 (2011).
[Crossref]

Belic, M. R.

S. L. Xu, N. Z. Petrovic, M. R. Belić, and W. W. Deng, “Exact solutions for the quintic nonlinear Schrödinger equation with time and space,” Nonlinear Dyn. 84(1), 251–259 (2016).
[Crossref]

S. L. Xu, J. X. Cheng, M. R. Belić, Z. L. Hu, and Y. Zhao, “Dynamics of nonlinear waves in two-dimensional cubic-quintic nonlinear Schrödinger equation with spatially modulated nonlinearities and potentials,” Opt. Express 24(9), 10066–10077 (2016).
[Crossref] [PubMed]

S. L. Xu, G. P. Zhou, N. Z. Petrović, and M. R. Belić, “Nonautonomous vector matter waves in two-component Bose-Einstein condensates with combined time-dependent harmonic-lattice potential,” J. Opt. 17(10), 105605 (2015).
[Crossref]

S. L. Xu and M. R. Belic, “Light bullets in coupled nonlinear Schrödinger equation with spatially modulated coefficients and Bessel trapping potential,” J. Mod. Opt. 62(9), 683–692 (2015).
[Crossref]

S. L. Xu, M. R. Belić, and W. P. Zhong, “Three-dimensional spatio-temporal vector solitary waves in coupled nonlinear Schrödinger equations with variable coefficients,” J. Opt. Soc. Am. B 30(1), 113–122 (2013).
[Crossref]

Bergé, L.

L. Bergé, “Wave collapse in physics: principles and applications to light and plasma waves,” Phys. Rep. 303(5-6), 259–370 (1998).
[Crossref]

L. Bergé, “Wave collapse in physics: principles and applications to light and plasma waves,” Phys. Rep. 303(5-6), 259–370 (1998).
[Crossref]

Biancalana, F.

T. X. Tran and F. Biancalana, “Diffractive resonant radiation emitted by spatial solitons in waveguide arrays,” Phys. Rev. Lett. 110(11), 113903 (2013).
[Crossref] [PubMed]

Bidasyuk, Y. M.

A. I. Yakimenko, S. I. Vilchinskii, Y. M. Bidasyuk, Y. I. Kuriatnikov, K. O. Isaieva, and M. Weyrauch, “Generation and decay of persistent currents in a toroidal Bose-Einstein condensate,” Rom. Rep. Phys. 67, 249–272 (2015).

Blaauboer, M.

M. Blaauboer, B. A. Malomed, and G. Kurizki, “Spatiotemporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84(9), 1906–1909 (2000).
[Crossref] [PubMed]

Buryak, A. V.

D. Mihalache, D. Mazilu, L. C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref] [PubMed]

Cardoso, W. B.

A. T. Avelar, D. Bazeia, and W. B. Cardoso, “Solitons with cubic and quintic nonlinearities modulated in space and time,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 025602 (2009).
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Chen, Y. F.

Y. F. Chen, K. Beckwitt, F. W. Wise, and B. A. Malomed, “Criteria for the experimental observation of multidimensional optical solitons in saturable media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046610 (2004).
[Crossref] [PubMed]

Cheng, J. X.

Christodoulides, D. N.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
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Cohen, O.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
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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(2), 023902 (2005).
[Crossref] [PubMed]

L. C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, “Soliton “molecules”: robust clusters of spatiotemporal optical solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046610 (2003).
[Crossref] [PubMed]

D. Mihalache, D. Mazilu, L. C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref] [PubMed]

Dehghan, M.

M. Dehghan and D. Mirzaei, “The dual reciprocity boundary element method (DRBEM) for two-dimensional sine-Gordon equation,” Comput. Methods Appl. Mech. Eng. 197(6-8), 476–486 (2008).
[Crossref]

Deng, W. W.

S. L. Xu, N. Z. Petrovic, M. R. Belić, and W. W. Deng, “Exact solutions for the quintic nonlinear Schrödinger equation with time and space,” Nonlinear Dyn. 84(1), 251–259 (2016).
[Crossref]

Denz, C.

C. Weilnau, M. Ahles, J. Petter, D. Träger, J. Schröder, and C. Denz, “Spatial optical (2+1)-dimensional scalar- and vector solitons in saturable nonlinear media,” Ann. Phys. 11(8), 573–629 (2002).
[Crossref]

Desyatnikov, A. S.

A. S. Desyatnikov and Y. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87(3), 033901 (2001).
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Dreisow, F.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78(3), 031801 (2008).
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D. E. Edmundson and R. H. Enns, “Particlelike nature of colliding three-dimensional optical solitons,” Phys. Rev. A 51(3), 2491–2498 (1995).
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N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
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Enns, R. H.

D. E. Edmundson and R. H. Enns, “Particlelike nature of colliding three-dimensional optical solitons,” Phys. Rev. A 51(3), 2491–2498 (1995).
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Fleischer, J. W.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
[Crossref] [PubMed]

Frantzeskakis, D. J.

V. S. Bagnato, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and D. Mihalache, “Bose-Einstein condensation: Twenty years after,” Rom. Rep. Phys. 67, 5–50 (2015).

D. J. Frantzeskakis, H. Leblond, and D. Mihalache, “Nonlinear optics of intense few-cycle pulses: An overview of recent theoretical and experimental developments,” Rom. J. Phys. 59, 767–784 (2014).

Gallo, K.

K. Gallo, A. Pasquazi, S. Stivala, and G. Assanto, “Parametric solitons in two-dimensional lattices of purely nonlinear origin,” Phys. Rev. Lett. 100(5), 053901 (2008).
[Crossref] [PubMed]

Garanovich, I. L.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78(3), 031801 (2008).
[Crossref]

Ge, L.

S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in PT-symmetric optical lattices,” Phys. Rev. A 85(2), 023822 (2012).
[Crossref]

Gorbach, A. V.

A. V. Gorbach and D. V. Skryabin, “Spatial solitons in periodic nanostructures,” Phys. Rev. A 79(5), 053812 (2009).
[Crossref]

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A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78(3), 031801 (2008).
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R. Hirota, “Exact Solution of the Korteweg-de Vries Equation for Multiple Collisions of Solitons,” Phys. Rev. Lett. 27(18), 1192–1194 (1971).
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Huang, T.

W. P. Zhong, M. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Self-trapping of scalar and vector dipole solitary waves in Kerr media,” Phys. Rev. A 83(4), 043833 (2011).
[Crossref]

Hudock, J.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
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Isaieva, K. O.

A. I. Yakimenko, S. I. Vilchinskii, Y. M. Bidasyuk, Y. I. Kuriatnikov, K. O. Isaieva, and M. Weyrauch, “Generation and decay of persistent currents in a toroidal Bose-Einstein condensate,” Rom. Rep. Phys. 67, 249–272 (2015).

A. I. Yakimenko, K. O. Isaieva, S. I. Vilchinskii, and M. Weyrauch, “Stability of persistent currents in spinor Bose-Einstein condensates,” Phys. Rev. A 88(5), 051602 (2013).
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Kartashov, Y. V.

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(2), 023902 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in bessel optical lattices,” Phys. Rev. Lett. 93(9), 093904 (2004).
[Crossref] [PubMed]

L. C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, “Soliton “molecules”: robust clusters of spatiotemporal optical solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046610 (2003).
[Crossref] [PubMed]

Kevrekidis, P. G.

V. S. Bagnato, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and D. Mihalache, “Bose-Einstein condensation: Twenty years after,” Rom. Rep. Phys. 67, 5–50 (2015).

Kivshar, Y. S.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78(3), 031801 (2008).
[Crossref]

L. C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, “Soliton “molecules”: robust clusters of spatiotemporal optical solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046610 (2003).
[Crossref] [PubMed]

A. S. Desyatnikov and Y. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87(3), 033901 (2001).
[Crossref] [PubMed]

Krolikowski, W.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78(3), 031801 (2008).
[Crossref]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046619 (2002).
[Crossref] [PubMed]

Królikowski, W.

W. Królikowski and O. Bang, “Solitons in nonlocal nonlinear media: exact solutions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(1 Pt 2), 016610 (2001).
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Kuriatnikov, Y. I.

A. I. Yakimenko, S. I. Vilchinskii, Y. M. Bidasyuk, Y. I. Kuriatnikov, K. O. Isaieva, and M. Weyrauch, “Generation and decay of persistent currents in a toroidal Bose-Einstein condensate,” Rom. Rep. Phys. 67, 249–272 (2015).

Kurizki, G.

M. Blaauboer, B. A. Malomed, and G. Kurizki, “Spatiotemporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84(9), 1906–1909 (2000).
[Crossref] [PubMed]

Lashkin, V. M.

A. I. Yakimenko, Y. A. Zaliznyak, and V. M. Lashkin, “Two-dimensional nonlinear vector states in Bose-Einstein condensates,” Phys. Rev. A 79(4), 043629 (2009).
[Crossref]

Leblond, H.

D. J. Frantzeskakis, H. Leblond, and D. Mihalache, “Nonlinear optics of intense few-cycle pulses: An overview of recent theoretical and experimental developments,” Rom. J. Phys. 59, 767–784 (2014).

Lederer, F.

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(2), 023902 (2005).
[Crossref] [PubMed]

D. Mihalache, D. Mazilu, L. C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref] [PubMed]

Liu, W. M.

D. S. Wang, S. W. Song, B. Xiong, and W. M. Liu, “Quantized vortices in a rotating Bose-Einstein condensate with spatiotemporally modulated interaction,” Phys. Rev. A 84(5), 053607 (2011).
[Crossref]

Liu, X.

X. Liu, K. Beckwitt, and F. Wise, “Generation of optical spatiotemporal solitons,” Opt. Photonics News 82, 4631–4634 (1999).

Malomed, B.

B. Malomed, L. Torner, F. Wise, and D. Mihalache, “On multidimensional solitons and their legacy in contemporary Atomic, Molecular and Optical physics,” J. Phys. At. Mol. Opt. Phys. 49(17), 170502 (2016).
[Crossref]

Malomed, B. A.

V. S. Bagnato, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and D. Mihalache, “Bose-Einstein condensation: Twenty years after,” Rom. Rep. Phys. 67, 5–50 (2015).

W. P. Zhong, M. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Self-trapping of scalar and vector dipole solitary waves in Kerr media,” Phys. Rev. A 83(4), 043833 (2011).
[Crossref]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B Quantum Semiclassical Opt. 7(5), R53–R72 (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(2), 023902 (2005).
[Crossref] [PubMed]

Y. F. Chen, K. Beckwitt, F. W. Wise, and B. A. Malomed, “Criteria for the experimental observation of multidimensional optical solitons in saturable media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046610 (2004).
[Crossref] [PubMed]

D. Mihalache, D. Mazilu, L. C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref] [PubMed]

M. Blaauboer, B. A. Malomed, and G. Kurizki, “Spatiotemporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84(9), 1906–1909 (2000).
[Crossref] [PubMed]

Manakov, S. V.

S. V. Manakov, “Theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974).

Mazilu, D.

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(2), 023902 (2005).
[Crossref] [PubMed]

D. Mihalache, D. Mazilu, L. C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref] [PubMed]

Mihalache, D.

B. Malomed, L. Torner, F. Wise, and D. Mihalache, “On multidimensional solitons and their legacy in contemporary Atomic, Molecular and Optical physics,” J. Phys. At. Mol. Opt. Phys. 49(17), 170502 (2016).
[Crossref]

V. S. Bagnato, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and D. Mihalache, “Bose-Einstein condensation: Twenty years after,” Rom. Rep. Phys. 67, 5–50 (2015).

D. J. Frantzeskakis, H. Leblond, and D. Mihalache, “Nonlinear optics of intense few-cycle pulses: An overview of recent theoretical and experimental developments,” Rom. J. Phys. 59, 767–784 (2014).

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B Quantum Semiclassical Opt. 7(5), R53–R72 (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(2), 023902 (2005).
[Crossref] [PubMed]

L. C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, “Soliton “molecules”: robust clusters of spatiotemporal optical solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046610 (2003).
[Crossref] [PubMed]

D. Mihalache, D. Mazilu, L. C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref] [PubMed]

Minovich, A.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78(3), 031801 (2008).
[Crossref]

Mirzaei, D.

M. Dehghan and D. Mirzaei, “The dual reciprocity boundary element method (DRBEM) for two-dimensional sine-Gordon equation,” Comput. Methods Appl. Mech. Eng. 197(6-8), 476–486 (2008).
[Crossref]

Mitchell, A.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78(3), 031801 (2008).
[Crossref]

Neshev, D. N.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78(3), 031801 (2008).
[Crossref]

Nixon, S.

S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in PT-symmetric optical lattices,” Phys. Rev. A 85(2), 023822 (2012).
[Crossref]

Nolte, S.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78(3), 031801 (2008).
[Crossref]

Papazoglou, D. G.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

Pasquazi, A.

K. Gallo, A. Pasquazi, S. Stivala, and G. Assanto, “Parametric solitons in two-dimensional lattices of purely nonlinear origin,” Phys. Rev. Lett. 100(5), 053901 (2008).
[Crossref] [PubMed]

Pérez-García, V. M.

L. C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, “Soliton “molecules”: robust clusters of spatiotemporal optical solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046610 (2003).
[Crossref] [PubMed]

Pertsch, T.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78(3), 031801 (2008).
[Crossref]

Petrovic, N. Z.

S. L. Xu, N. Z. Petrovic, M. R. Belić, and W. W. Deng, “Exact solutions for the quintic nonlinear Schrödinger equation with time and space,” Nonlinear Dyn. 84(1), 251–259 (2016).
[Crossref]

S. L. Xu, G. P. Zhou, N. Z. Petrović, and M. R. Belić, “Nonautonomous vector matter waves in two-component Bose-Einstein condensates with combined time-dependent harmonic-lattice potential,” J. Opt. 17(10), 105605 (2015).
[Crossref]

Petter, J.

C. Weilnau, M. Ahles, J. Petter, D. Träger, J. Schröder, and C. Denz, “Spatial optical (2+1)-dimensional scalar- and vector solitons in saturable nonlinear media,” Ann. Phys. 11(8), 573–629 (2002).
[Crossref]

Rasmussen, J. J.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046619 (2002).
[Crossref] [PubMed]

Schröder, J.

C. Weilnau, M. Ahles, J. Petter, D. Träger, J. Schröder, and C. Denz, “Spatial optical (2+1)-dimensional scalar- and vector solitons in saturable nonlinear media,” Ann. Phys. 11(8), 573–629 (2002).
[Crossref]

Segev, M.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
[Crossref] [PubMed]

Silberberg, Y.

Skryabin, D. V.

A. V. Gorbach and D. V. Skryabin, “Spatial solitons in periodic nanostructures,” Phys. Rev. A 79(5), 053812 (2009).
[Crossref]

Song, S. W.

D. S. Wang, S. W. Song, B. Xiong, and W. M. Liu, “Quantized vortices in a rotating Bose-Einstein condensate with spatiotemporally modulated interaction,” Phys. Rev. A 84(5), 053607 (2011).
[Crossref]

Stivala, S.

K. Gallo, A. Pasquazi, S. Stivala, and G. Assanto, “Parametric solitons in two-dimensional lattices of purely nonlinear origin,” Phys. Rev. Lett. 100(5), 053901 (2008).
[Crossref] [PubMed]

Sukhorukov, A. A.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78(3), 031801 (2008).
[Crossref]

Suntsov, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

Szameit, A.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78(3), 031801 (2008).
[Crossref]

Torner, L.

B. Malomed, L. Torner, F. Wise, and D. Mihalache, “On multidimensional solitons and their legacy in contemporary Atomic, Molecular and Optical physics,” J. Phys. At. Mol. Opt. Phys. 49(17), 170502 (2016).
[Crossref]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B Quantum Semiclassical Opt. 7(5), R53–R72 (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(2), 023902 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in bessel optical lattices,” Phys. Rev. Lett. 93(9), 093904 (2004).
[Crossref] [PubMed]

L. C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, “Soliton “molecules”: robust clusters of spatiotemporal optical solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046610 (2003).
[Crossref] [PubMed]

D. Mihalache, D. Mazilu, L. C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref] [PubMed]

Torres, J. P.

D. Mihalache, D. Mazilu, L. C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref] [PubMed]

Towers, I.

D. Mihalache, D. Mazilu, L. C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref] [PubMed]

Träger, D.

C. Weilnau, M. Ahles, J. Petter, D. Träger, J. Schröder, and C. Denz, “Spatial optical (2+1)-dimensional scalar- and vector solitons in saturable nonlinear media,” Ann. Phys. 11(8), 573–629 (2002).
[Crossref]

Tran, T. X.

T. X. Tran and F. Biancalana, “Diffractive resonant radiation emitted by spatial solitons in waveguide arrays,” Phys. Rev. Lett. 110(11), 113903 (2013).
[Crossref] [PubMed]

Tünnermann, A.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78(3), 031801 (2008).
[Crossref]

Tzortzakis, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

Vilchinskii, S. I.

A. I. Yakimenko, S. I. Vilchinskii, Y. M. Bidasyuk, Y. I. Kuriatnikov, K. O. Isaieva, and M. Weyrauch, “Generation and decay of persistent currents in a toroidal Bose-Einstein condensate,” Rom. Rep. Phys. 67, 249–272 (2015).

A. I. Yakimenko, K. O. Isaieva, S. I. Vilchinskii, and M. Weyrauch, “Stability of persistent currents in spinor Bose-Einstein condensates,” Phys. Rev. A 88(5), 051602 (2013).
[Crossref]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in bessel optical lattices,” Phys. Rev. Lett. 93(9), 093904 (2004).
[Crossref] [PubMed]

Wang, D. S.

D. S. Wang, S. W. Song, B. Xiong, and W. M. Liu, “Quantized vortices in a rotating Bose-Einstein condensate with spatiotemporally modulated interaction,” Phys. Rev. A 84(5), 053607 (2011).
[Crossref]

Weilnau, C.

C. Weilnau, M. Ahles, J. Petter, D. Träger, J. Schröder, and C. Denz, “Spatial optical (2+1)-dimensional scalar- and vector solitons in saturable nonlinear media,” Ann. Phys. 11(8), 573–629 (2002).
[Crossref]

Weyrauch, M.

A. I. Yakimenko, S. I. Vilchinskii, Y. M. Bidasyuk, Y. I. Kuriatnikov, K. O. Isaieva, and M. Weyrauch, “Generation and decay of persistent currents in a toroidal Bose-Einstein condensate,” Rom. Rep. Phys. 67, 249–272 (2015).

A. I. Yakimenko, K. O. Isaieva, S. I. Vilchinskii, and M. Weyrauch, “Stability of persistent currents in spinor Bose-Einstein condensates,” Phys. Rev. A 88(5), 051602 (2013).
[Crossref]

Wise, F.

B. Malomed, L. Torner, F. Wise, and D. Mihalache, “On multidimensional solitons and their legacy in contemporary Atomic, Molecular and Optical physics,” J. Phys. At. Mol. Opt. Phys. 49(17), 170502 (2016).
[Crossref]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

X. Liu, K. Beckwitt, and F. Wise, “Generation of optical spatiotemporal solitons,” Opt. Photonics News 82, 4631–4634 (1999).

Wise, F. W.

Y. F. Chen, K. Beckwitt, F. W. Wise, and B. A. Malomed, “Criteria for the experimental observation of multidimensional optical solitons in saturable media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046610 (2004).
[Crossref] [PubMed]

Wyller, J.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046619 (2002).
[Crossref] [PubMed]

Xiong, B.

D. S. Wang, S. W. Song, B. Xiong, and W. M. Liu, “Quantized vortices in a rotating Bose-Einstein condensate with spatiotemporally modulated interaction,” Phys. Rev. A 84(5), 053607 (2011).
[Crossref]

Xu, S. L.

S. L. Xu, N. Z. Petrovic, M. R. Belić, and W. W. Deng, “Exact solutions for the quintic nonlinear Schrödinger equation with time and space,” Nonlinear Dyn. 84(1), 251–259 (2016).
[Crossref]

S. L. Xu, J. X. Cheng, M. R. Belić, Z. L. Hu, and Y. Zhao, “Dynamics of nonlinear waves in two-dimensional cubic-quintic nonlinear Schrödinger equation with spatially modulated nonlinearities and potentials,” Opt. Express 24(9), 10066–10077 (2016).
[Crossref] [PubMed]

S. L. Xu and M. R. Belic, “Light bullets in coupled nonlinear Schrödinger equation with spatially modulated coefficients and Bessel trapping potential,” J. Mod. Opt. 62(9), 683–692 (2015).
[Crossref]

S. L. Xu, G. P. Zhou, N. Z. Petrović, and M. R. Belić, “Nonautonomous vector matter waves in two-component Bose-Einstein condensates with combined time-dependent harmonic-lattice potential,” J. Opt. 17(10), 105605 (2015).
[Crossref]

S. L. Xu, M. R. Belić, and W. P. Zhong, “Three-dimensional spatio-temporal vector solitary waves in coupled nonlinear Schrödinger equations with variable coefficients,” J. Opt. Soc. Am. B 30(1), 113–122 (2013).
[Crossref]

Yakimenko, A. I.

A. I. Yakimenko, S. I. Vilchinskii, Y. M. Bidasyuk, Y. I. Kuriatnikov, K. O. Isaieva, and M. Weyrauch, “Generation and decay of persistent currents in a toroidal Bose-Einstein condensate,” Rom. Rep. Phys. 67, 249–272 (2015).

A. I. Yakimenko, K. O. Isaieva, S. I. Vilchinskii, and M. Weyrauch, “Stability of persistent currents in spinor Bose-Einstein condensates,” Phys. Rev. A 88(5), 051602 (2013).
[Crossref]

A. I. Yakimenko, Y. A. Zaliznyak, and V. M. Lashkin, “Two-dimensional nonlinear vector states in Bose-Einstein condensates,” Phys. Rev. A 79(4), 043629 (2009).
[Crossref]

Yang, J.

S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in PT-symmetric optical lattices,” Phys. Rev. A 85(2), 023822 (2012).
[Crossref]

Zaliznyak, Y. A.

A. I. Yakimenko, Y. A. Zaliznyak, and V. M. Lashkin, “Two-dimensional nonlinear vector states in Bose-Einstein condensates,” Phys. Rev. A 79(4), 043629 (2009).
[Crossref]

Zhao, Y.

Zhong, W. P.

S. L. Xu, M. R. Belić, and W. P. Zhong, “Three-dimensional spatio-temporal vector solitary waves in coupled nonlinear Schrödinger equations with variable coefficients,” J. Opt. Soc. Am. B 30(1), 113–122 (2013).
[Crossref]

W. P. Zhong, M. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Self-trapping of scalar and vector dipole solitary waves in Kerr media,” Phys. Rev. A 83(4), 043833 (2011).
[Crossref]

Zhong, W.-P.

W.-P. Zhong and M. Belic, “Resonance solitons produced by azimuthal modulation in self-focusing and self-defocusing materials,” Nonlinear Dyn. 73(4), 2091–2102 (2013).
[Crossref]

Zhou, G. P.

S. L. Xu, G. P. Zhou, N. Z. Petrović, and M. R. Belić, “Nonautonomous vector matter waves in two-component Bose-Einstein condensates with combined time-dependent harmonic-lattice potential,” J. Opt. 17(10), 105605 (2015).
[Crossref]

Ann. Phys. (1)

C. Weilnau, M. Ahles, J. Petter, D. Träger, J. Schröder, and C. Denz, “Spatial optical (2+1)-dimensional scalar- and vector solitons in saturable nonlinear media,” Ann. Phys. 11(8), 573–629 (2002).
[Crossref]

Comput. Methods Appl. Mech. Eng. (1)

M. Dehghan and D. Mirzaei, “The dual reciprocity boundary element method (DRBEM) for two-dimensional sine-Gordon equation,” Comput. Methods Appl. Mech. Eng. 197(6-8), 476–486 (2008).
[Crossref]

J. Mod. Opt. (1)

S. L. Xu and M. R. Belic, “Light bullets in coupled nonlinear Schrödinger equation with spatially modulated coefficients and Bessel trapping potential,” J. Mod. Opt. 62(9), 683–692 (2015).
[Crossref]

J. Opt. (1)

S. L. Xu, G. P. Zhou, N. Z. Petrović, and M. R. Belić, “Nonautonomous vector matter waves in two-component Bose-Einstein condensates with combined time-dependent harmonic-lattice potential,” J. Opt. 17(10), 105605 (2015).
[Crossref]

J. Opt. B Quantum Semiclassical Opt. (1)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

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

J. Phys. At. Mol. Opt. Phys. (1)

B. Malomed, L. Torner, F. Wise, and D. Mihalache, “On multidimensional solitons and their legacy in contemporary Atomic, Molecular and Optical physics,” J. Phys. At. Mol. Opt. Phys. 49(17), 170502 (2016).
[Crossref]

Nonlinear Dyn. (2)

W.-P. Zhong and M. Belic, “Resonance solitons produced by azimuthal modulation in self-focusing and self-defocusing materials,” Nonlinear Dyn. 73(4), 2091–2102 (2013).
[Crossref]

S. L. Xu, N. Z. Petrovic, M. R. Belić, and W. W. Deng, “Exact solutions for the quintic nonlinear Schrödinger equation with time and space,” Nonlinear Dyn. 84(1), 251–259 (2016).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Opt. Photonics News (1)

X. Liu, K. Beckwitt, and F. Wise, “Generation of optical spatiotemporal solitons,” Opt. Photonics News 82, 4631–4634 (1999).

Phys. Rep. (2)

L. Bergé, “Wave collapse in physics: principles and applications to light and plasma waves,” Phys. Rep. 303(5-6), 259–370 (1998).
[Crossref]

L. Bergé, “Wave collapse in physics: principles and applications to light and plasma waves,” Phys. Rep. 303(5-6), 259–370 (1998).
[Crossref]

Phys. Rev. A (8)

D. E. Edmundson and R. H. Enns, “Particlelike nature of colliding three-dimensional optical solitons,” Phys. Rev. A 51(3), 2491–2498 (1995).
[Crossref] [PubMed]

S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in PT-symmetric optical lattices,” Phys. Rev. A 85(2), 023822 (2012).
[Crossref]

W. P. Zhong, M. Belić, G. Assanto, B. A. Malomed, and T. Huang, “Self-trapping of scalar and vector dipole solitary waves in Kerr media,” Phys. Rev. A 83(4), 043833 (2011).
[Crossref]

A. V. Gorbach and D. V. Skryabin, “Spatial solitons in periodic nanostructures,” Phys. Rev. A 79(5), 053812 (2009).
[Crossref]

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78(3), 031801 (2008).
[Crossref]

D. S. Wang, S. W. Song, B. Xiong, and W. M. Liu, “Quantized vortices in a rotating Bose-Einstein condensate with spatiotemporally modulated interaction,” Phys. Rev. A 84(5), 053607 (2011).
[Crossref]

A. I. Yakimenko, Y. A. Zaliznyak, and V. M. Lashkin, “Two-dimensional nonlinear vector states in Bose-Einstein condensates,” Phys. Rev. A 79(4), 043629 (2009).
[Crossref]

A. I. Yakimenko, K. O. Isaieva, S. I. Vilchinskii, and M. Weyrauch, “Stability of persistent currents in spinor Bose-Einstein condensates,” Phys. Rev. A 88(5), 051602 (2013).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (5)

A. T. Avelar, D. Bazeia, and W. B. Cardoso, “Solitons with cubic and quintic nonlinearities modulated in space and time,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 025602 (2009).
[Crossref] [PubMed]

Y. F. Chen, K. Beckwitt, F. W. Wise, and B. A. Malomed, “Criteria for the experimental observation of multidimensional optical solitons in saturable media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046610 (2004).
[Crossref] [PubMed]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046619 (2002).
[Crossref] [PubMed]

W. Królikowski and O. Bang, “Solitons in nonlocal nonlinear media: exact solutions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(1 Pt 2), 016610 (2001).
[PubMed]

L. C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, “Soliton “molecules”: robust clusters of spatiotemporal optical solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046610 (2003).
[Crossref] [PubMed]

Phys. Rev. Lett. (10)

K. Gallo, A. Pasquazi, S. Stivala, and G. Assanto, “Parametric solitons in two-dimensional lattices of purely nonlinear origin,” Phys. Rev. Lett. 100(5), 053901 (2008).
[Crossref] [PubMed]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

M. Blaauboer, B. A. Malomed, and G. Kurizki, “Spatiotemporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84(9), 1906–1909 (2000).
[Crossref] [PubMed]

D. Mihalache, D. Mazilu, L. C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref] [PubMed]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
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Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in bessel optical lattices,” Phys. Rev. Lett. 93(9), 093904 (2004).
[Crossref] [PubMed]

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(2), 023902 (2005).
[Crossref] [PubMed]

T. X. Tran and F. Biancalana, “Diffractive resonant radiation emitted by spatial solitons in waveguide arrays,” Phys. Rev. Lett. 110(11), 113903 (2013).
[Crossref] [PubMed]

R. Hirota, “Exact Solution of the Korteweg-de Vries Equation for Multiple Collisions of Solitons,” Phys. Rev. Lett. 27(18), 1192–1194 (1971).
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A. S. Desyatnikov and Y. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87(3), 033901 (2001).
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Rom. J. Phys. (1)

D. J. Frantzeskakis, H. Leblond, and D. Mihalache, “Nonlinear optics of intense few-cycle pulses: An overview of recent theoretical and experimental developments,” Rom. J. Phys. 59, 767–784 (2014).

Rom. Rep. Phys. (2)

V. S. Bagnato, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and D. Mihalache, “Bose-Einstein condensation: Twenty years after,” Rom. Rep. Phys. 67, 5–50 (2015).

A. I. Yakimenko, S. I. Vilchinskii, Y. M. Bidasyuk, Y. I. Kuriatnikov, K. O. Isaieva, and M. Weyrauch, “Generation and decay of persistent currents in a toroidal Bose-Einstein condensate,” Rom. Rep. Phys. 67, 249–272 (2015).

Sov. Phys. JETP (1)

S. V. Manakov, “Theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974).

Other (3)

W. Torruellas, Y. S. Kivshar, and G. I. Stegeman, Quadratic Solitons (Springer, 2001).

D. Zwillinger, Handbook of Differential Equations, 3rd ed. (Academic, 1997).

T. I. Lakoba, “Stability analysis of the split-step Fourier method on the background of a soliton of the nonlinear Schrödinger equation,” in Methods for Partial Differential Equations, 4974, 641–649 (2010).

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Figures (6)

Fig. 1
Fig. 1

(a), (b) Distributions of the nonlinearity coefficient χ(r) and the trapping potential V(r) for n=1 . (c) and (d) Amplitude of the radial field distributions ψ j for different mode numbers, m=0,1,2 (c) and n=2,3,4 (d). Other parameters: q = 0 and η=0.4 .

Fig. 2
Fig. 2

Intensity distributions of 3D LBs | u 1 | 2 , | u 2 | 2 , and the total intensity from left to right, and for different l ( l=1,2,3 ) from top to bottom, at z=70 . Parameters: m = 1, n=1 , q=0.1 . Other parameters are as in Fig. 1.

Fig. 3
Fig. 3

Same as Fig. 2 but for different m ( m=0,2,3 ), from top to bottom at z=70 . The parameters are same as in Fig. 1, but for l=3 , from left to right.

Fig. 4
Fig. 4

Evolution of the stable 3D LB distribution ψ 1 for m=l=2 , q = 0.5, and n=1,2,3 from left to right.

Fig. 5
Fig. 5

Same as Fig. 4 but for m=n=3 , and q=0,0.5,1 from left to right.

Fig. 6
Fig. 6

Evolution of 3D LB distributions and linear stability spectra of the condensate ψ 1 against the perturbation with an initial random noise of level 10%, at different propagation distances. The first column z=0 , the second and the third columns z=600 . The fourth column presents the linear stability spectra. Top: m=0 , n=1 ; middle: m=n=1 ; bottom: m=1 , n=2 . Other parameters are the same as in Fig. 1.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

i u j z + 1 2 2 u j +χ(r)I u j +V(r) u j =0,
1 Y j [ 1 sinθ θ (sinθ θ ) Y j + 1 sin 2 θ 2 Y j φ 2 ]=l(l+1),
2 r 2 ψ [ i ψ z + 1 2 ( 2 r ψ r + 2 ψ r 2 )+χ(r) | ψ | 2 ψ+Vψ ]=l(l+1),
a 1 = (1+ q 2 ) 1/2 , b 1 =iq a 1 ,
a 2 =q a 1 , b 2 =±i a 1 ,
1 2 d U 2 d R 2 +EU+ χ 0 U 3 =0
U(R)= 2E sech( 2E R).
χ 0 = χ 2 r 4 ρ 6 , R z + R r ϕ r =0
ρ z + 1 2 ( ρ 2 ϕ r 2 +2 ρ r ϕ r + 2ρ r ϕ r )=0,
ρ ϕ z + 1 2 [ 2 ρ r 2 ρ ( ϕ r ) 2 + 2 r ρ r ρ m 2 r 2 ]+Vρ=0,
2 ρ r R r +ρ 2 R r 2 + 2ρ r R r =0,
θ 1 d 2 f d θ 1 2 +( m+ 3 2 θ 1 ) df d θ 1 +nf=0,
u j = Kκ w 0 3/2 ( r w 0 ) m ( a n cosmφ+ b n sinmφ ) P l m (cosθ)f( θ 1 )U(R) e r 2 2 w 0 +i( b 0 2n+m+1 w 0 2 z ) .
u j (x,y,τ,z)= e -iλz [ u 0j (x,y,τ)+ μ j (x,y,τ) e iδz + v j * (x,y,τ) e i δ * z ],
( L j B A A B L j A A A A L 3j C A A C L 3j )( μ 1 v 1 μ 2 v 2 )=δ( μ 1 v 1 μ 2 v 2 ),