Abstract

An analytical solitary wave solution to the generalized nonlinear Schrödinger equation (NLSE) with varying coefficients in Bessel optical lattices is obtained based on the self-similar method. Our results indicate that a new family of Bessel (BSL) self-similar spatial solitons can be formed in the Kerr nonlinear media in the confined cylindrical symmetric geometry in sizes. These soliton profiles are rather stable, independent of propagation distance.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]

2009 (1)

J. Liang, H. Liu, F. Liu, and L. Yi, “Analytical solutions to the fully extended nonlinear Schrödinger equation,” J. Phys. A: Math. Theor. 42, 335204 (2009).
[CrossRef]

2008 (2)

L. Dong, H. Wang, W. Zhou, X. Yang, X. Lv, and H. Ch, “Necklace solitons and ring solitons in Bessel optical lattices,” Opt. Express 16, 5649-5655 (2008).
[CrossRef] [PubMed]

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

2007 (1)

W. P. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75, 061801 (2007).
[CrossRef]

2006 (2)

2005 (6)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable ring-profile vortex solitons in Bessel optical lattices,” Phys. Rev. Lett. 94, 043902 (2005).
[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, 023902 (2005).
[CrossRef] [PubMed]

S. H. Chen, L. Yi, D. S. Guo, and P. X. Lu, “Chirped self-similar solutions of a generalized nonlinear Schrödinger equation model,” Phys. Rev. E 71, 016606 (2005).
[CrossRef]

S. H. Chen and L. Yi, “Self-similar evolutions of parabolic, Hermite-Gaussian, and hybrid optical pulses: Universality and diversity,” Phys. Rev. E 72, 016622 (2005).
[CrossRef]

C. H. Tenorio, E. V. Vargas, V. N. Serkin, M. A. Granados, T. L. Belyaeva, R. P. Moreno, and L. M. Lara, “Dynamics of solitons in the model of nonlinear Schrödinger equation with an external harmonic potential,” IEEE J. Quantum Electron. 35, 778-786 (2005).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Topological dragging of solitons,” Phys. Rev. Lett. 95, 243902 (2005).
[CrossRef] [PubMed]

2004 (6)

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, “Spatial soliton switching in quasi-continuous optical arrays,” Opt. Lett. 24, 766-768 (2004).
[CrossRef]

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

Z. Chen, H. Martin, E. D. Eugenieva, J. J. Xu, and A. Bezryadina1, “Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains,” Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton trains in photonic lattices,” Opt. Express 12, 2831-2837 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

2003 (6)

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. 28, 710-712 (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, 213906-213909 (2003).
[CrossRef] [PubMed]

J. Yang, Z. H. Musslimani, and H. Ziad, “Fundamental and vortex solitons in a two-dimensional optical lattice,” Opt. Lett. 28, 2094-2096 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

N. Chattrapiban, E. A. Rogers, D. Cofield, W. T. Hill, III, and R. Roy, “Generation of nondiffracting Bessel beams by use of a spatial light modulator,” Opt. Lett. 28, 2183-2185 (2003).
[CrossRef] [PubMed]

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90, 113902 (2003).
[CrossRef] [PubMed]

2002 (2)

A. S. Desyatnikov, D. Neshev, E. A. Ostrovskaya, and Y. S. Kivshar, “Multipole composite spatial solitons: theory and experiment,” J. Opt. Soc. Am. B 19, 586-595 (2002).
[CrossRef]

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

2001 (1)

B. A. Malomed and P. G. Kevrekidis, “Discrete vortex solitons,” Phys. Rev. E 64, 026601 (2001).
[CrossRef]

2000 (4)

V. N. Serkin and A. Hasegawa, “Novel soliton solutions of the nonlinear Schrödinger equation model,” Phys. Rev. Lett. 85, 4502-4505 (2000).
[CrossRef] [PubMed]

M. Soljacic, M. Segev, and C. R. Menyuk, “Self-similarity and fractals in soliton-supporting systems,” Phys. Rev. E 61, R1048-R1051 (2000).
[CrossRef]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010-6013 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

1999 (1)

R. Morandotti, U. Peschel, and J. S. Aitchison, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett. 83, 2726-2729 (1999).
[CrossRef]

1998 (1)

1993 (1)

1992 (1)

C. R. Menyuk, D. Levi, and P. Winternitz, “Self-similarity in transient stimulated Raman scattering,” Phys. Rev. Lett. 69, 3048-3051 (1992).
[CrossRef] [PubMed]

1991 (1)

1988 (1)

Agrawal, G. P.

S. A. Ponomarenko and G. P. Agrawal, “Do solitonlike self-similar waves exist in nonlinear optical media?” Phys. Rev. Lett. 97, 013901 (2006).
[CrossRef] [PubMed]

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, and J. S. Aitchison, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett. 83, 2726-2729 (1999).
[CrossRef]

An, S.

Anderson, D.

Barenblatt, G. I.

G. I. Barenblatt, Scaling, Self-Similarity, and Intermediate Asymptotics (Cambridge Univ. Press, 1996).

Belic, M.

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

Belyaeva, T. L.

C. H. Tenorio, E. V. Vargas, V. N. Serkin, M. A. Granados, T. L. Belyaeva, R. P. Moreno, and L. M. Lara, “Dynamics of solitons in the model of nonlinear Schrödinger equation with an external harmonic potential,” IEEE J. Quantum Electron. 35, 778-786 (2005).
[CrossRef]

Bezryadina1, A.

Z. Chen, H. Martin, E. D. Eugenieva, J. J. Xu, and A. Bezryadina1, “Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains,” Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

Brauer, A.

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

Buckley, J. R.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Carmon, T.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Ch, H.

Chattrapiban, N.

Chen, G.

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

Chen, S. H.

S. H. Chen, L. Yi, D. S. Guo, and P. X. Lu, “Chirped self-similar solutions of a generalized nonlinear Schrödinger equation model,” Phys. Rev. E 71, 016606 (2005).
[CrossRef]

S. H. Chen and L. Yi, “Self-similar evolutions of parabolic, Hermite-Gaussian, and hybrid optical pulses: Universality and diversity,” Phys. Rev. E 72, 016622 (2005).
[CrossRef]

Chen, Z.

Z. Chen, H. Martin, E. D. Eugenieva, J. J. Xu, and A. Bezryadina1, “Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains,” Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

Christodoulides, D. N.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (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, 213906-213909 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794-796 (1988).
[CrossRef] [PubMed]

Clark, W. G.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Cofield, D.

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, 213906-213909 (2003).
[CrossRef] [PubMed]

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] [PubMed]

de Sterke, C. M.

Denz, C.

Desaix, M.

Desyatnikov, A. S.

Dong, L.

Dudley, J. M.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010-6013 (2000).
[CrossRef] [PubMed]

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (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, 213906-213909 (2003).
[CrossRef] [PubMed]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

Eugenieva, E. D.

Z. Chen, H. Martin, E. D. Eugenieva, J. J. Xu, and A. Bezryadina1, “Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains,” Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

Fermann, M. E.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010-6013 (2000).
[CrossRef] [PubMed]

Fischer, R.

Fleischer, J. W.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (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, 213906-213909 (2003).
[CrossRef] [PubMed]

Glass, A. M.

A. M. Glass and J. Strait, “The photorefractive effect in semiconductors,” in Photorefractive Materials and their Applications I, P.Gunter and J.P.Huignard, eds. (Springer, 1988), p. 237(R)C262.

Granados, M. A.

C. H. Tenorio, E. V. Vargas, V. N. Serkin, M. A. Granados, T. L. Belyaeva, R. P. Moreno, and L. M. Lara, “Dynamics of solitons in the model of nonlinear Schrödinger equation with an external harmonic potential,” IEEE J. Quantum Electron. 35, 778-786 (2005).
[CrossRef]

Guo, D. S.

S. H. Chen, L. Yi, D. S. Guo, and P. X. Lu, “Chirped self-similar solutions of a generalized nonlinear Schrödinger equation model,” Phys. Rev. E 71, 016606 (2005).
[CrossRef]

Harvey, J. D.

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90, 113902 (2003).
[CrossRef] [PubMed]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010-6013 (2000).
[CrossRef] [PubMed]

Hasegawa, A.

V. N. Serkin and A. Hasegawa, “Novel soliton solutions of the nonlinear Schrödinger equation model,” Phys. Rev. Lett. 85, 4502-4505 (2000).
[CrossRef] [PubMed]

Hill, W. T.

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, 213906-213909 (2003).
[CrossRef] [PubMed]

Ilday, F. Ö.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Joseph, R. I.

Karlsson, M.

Karpman, V. I.

V. I. Karpman, Non-Linear Waves in Dispersive Media (Pergamon, 1975).

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Topological dragging of solitons,” Phys. Rev. Lett. 95, 243902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable ring-profile vortex solitons in Bessel optical lattices,” Phys. Rev. Lett. 94, 043902 (2005).
[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, 023902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, “Spatial soliton switching in quasi-continuous optical arrays,” Opt. Lett. 24, 766-768 (2004).
[CrossRef]

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

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton trains in photonic lattices,” Opt. Express 12, 2831-2837 (2004).
[CrossRef] [PubMed]

Kevrekidis, P. G.

B. A. Malomed and P. G. Kevrekidis, “Discrete vortex solitons,” Phys. Rev. E 64, 026601 (2001).
[CrossRef]

Kivshar, Y.

Kivshar, Y. S.

Krlikowski, W.

Krolikowski, W.

Kruglov, V. I.

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90, 113902 (2003).
[CrossRef] [PubMed]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010-6013 (2000).
[CrossRef] [PubMed]

Lara, L. M.

C. H. Tenorio, E. V. Vargas, V. N. Serkin, M. A. Granados, T. L. Belyaeva, R. P. Moreno, and L. M. Lara, “Dynamics of solitons in the model of nonlinear Schrödinger equation with an external harmonic potential,” IEEE J. Quantum Electron. 35, 778-786 (2005).
[CrossRef]

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, 023902 (2005).
[CrossRef] [PubMed]

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

Levi, D.

C. R. Menyuk, D. Levi, and P. Winternitz, “Self-similarity in transient stimulated Raman scattering,” Phys. Rev. Lett. 69, 3048-3051 (1992).
[CrossRef] [PubMed]

Liang, J.

J. Liang, H. Liu, F. Liu, and L. Yi, “Analytical solutions to the fully extended nonlinear Schrödinger equation,” J. Phys. A: Math. Theor. 42, 335204 (2009).
[CrossRef]

Lisak, M.

Liu, F.

J. Liang, H. Liu, F. Liu, and L. Yi, “Analytical solutions to the fully extended nonlinear Schrödinger equation,” J. Phys. A: Math. Theor. 42, 335204 (2009).
[CrossRef]

Liu, H.

J. Liang, H. Liu, F. Liu, and L. Yi, “Analytical solutions to the fully extended nonlinear Schrödinger equation,” J. Phys. A: Math. Theor. 42, 335204 (2009).
[CrossRef]

Lu, P. X.

S. H. Chen, L. Yi, D. S. Guo, and P. X. Lu, “Chirped self-similar solutions of a generalized nonlinear Schrödinger equation model,” Phys. Rev. E 71, 016606 (2005).
[CrossRef]

Lv, X.

Malomed, B. A.

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] [PubMed]

B. A. Malomed and P. G. Kevrekidis, “Discrete vortex solitons,” Phys. Rev. E 64, 026601 (2001).
[CrossRef]

Martin, H.

Z. Chen, H. Martin, E. D. Eugenieva, J. J. Xu, and A. Bezryadina1, “Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains,” Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

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, 023902 (2005).
[CrossRef] [PubMed]

Menyuk, C. R.

M. Soljacic, M. Segev, and C. R. Menyuk, “Self-similarity and fractals in soliton-supporting systems,” Phys. Rev. E 61, R1048-R1051 (2000).
[CrossRef]

C. R. Menyuk, D. Levi, and P. Winternitz, “Self-similarity in transient stimulated Raman scattering,” Phys. Rev. Lett. 69, 3048-3051 (1992).
[CrossRef] [PubMed]

Mihalache, 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, 023902 (2005).
[CrossRef] [PubMed]

Millar, P. D.

Monro, T. M.

Morandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, and J. S. Aitchison, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett. 83, 2726-2729 (1999).
[CrossRef]

Moreno, R. P.

C. H. Tenorio, E. V. Vargas, V. N. Serkin, M. A. Granados, T. L. Belyaeva, R. P. Moreno, and L. M. Lara, “Dynamics of solitons in the model of nonlinear Schrödinger equation with an external harmonic potential,” IEEE J. Quantum Electron. 35, 778-786 (2005).
[CrossRef]

Musslimani, Z. H.

Neshev, D.

Neshev, D. N.

Ostrovskaya, E.

Ostrovskaya, E. A.

Peacock, A. C.

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90, 113902 (2003).
[CrossRef] [PubMed]

Pertsch, T.

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

Peschel, U.

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

R. Morandotti, U. Peschel, and J. S. Aitchison, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett. 83, 2726-2729 (1999).
[CrossRef]

Poladian, L.

Ponomarenko, S. A.

S. A. Ponomarenko and G. P. Agrawal, “Do solitonlike self-similar waves exist in nonlinear optical media?” Phys. Rev. Lett. 97, 013901 (2006).
[CrossRef] [PubMed]

Quiroga-Teixeiro, M. L.

Richardson, S. M.

S. M. Richardson, Fluid Mechanics (Hemisphere Publishing Corp., 1989).

Rogers, E. A.

Roy, R.

Segev, M.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (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, 213906-213909 (2003).
[CrossRef] [PubMed]

M. Soljacic, M. Segev, and C. R. Menyuk, “Self-similarity and fractals in soliton-supporting systems,” Phys. Rev. E 61, R1048-R1051 (2000).
[CrossRef]

Serkin, V. N.

C. H. Tenorio, E. V. Vargas, V. N. Serkin, M. A. Granados, T. L. Belyaeva, R. P. Moreno, and L. M. Lara, “Dynamics of solitons in the model of nonlinear Schrödinger equation with an external harmonic potential,” IEEE J. Quantum Electron. 35, 778-786 (2005).
[CrossRef]

V. N. Serkin and A. Hasegawa, “Novel soliton solutions of the nonlinear Schrödinger equation model,” Phys. Rev. Lett. 85, 4502-4505 (2000).
[CrossRef] [PubMed]

Silberberg, Y.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

Sipe, J. E.

Soljacic, M.

M. Soljacic, M. Segev, and C. R. Menyuk, “Self-similarity and fractals in soliton-supporting systems,” Phys. Rev. E 61, R1048-R1051 (2000).
[CrossRef]

Strait, J.

A. M. Glass and J. Strait, “The photorefractive effect in semiconductors,” in Photorefractive Materials and their Applications I, P.Gunter and J.P.Huignard, eds. (Springer, 1988), p. 237(R)C262.

Sukhorukov, A. A.

Tenorio, C. H.

C. H. Tenorio, E. V. Vargas, V. N. Serkin, M. A. Granados, T. L. Belyaeva, R. P. Moreno, and L. M. Lara, “Dynamics of solitons in the model of nonlinear Schrödinger equation with an external harmonic potential,” IEEE J. Quantum Electron. 35, 778-786 (2005).
[CrossRef]

Thomsen, B. C.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010-6013 (2000).
[CrossRef] [PubMed]

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Topological dragging of solitons,” Phys. Rev. Lett. 95, 243902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable ring-profile vortex solitons in Bessel optical lattices,” Phys. Rev. Lett. 94, 043902 (2005).
[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, 023902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, “Spatial soliton switching in quasi-continuous optical arrays,” Opt. Lett. 24, 766-768 (2004).
[CrossRef]

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

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton trains in photonic lattices,” Opt. Express 12, 2831-2837 (2004).
[CrossRef] [PubMed]

Träger, D.

Vargas, E. V.

C. H. Tenorio, E. V. Vargas, V. N. Serkin, M. A. Granados, T. L. Belyaeva, R. P. Moreno, and L. M. Lara, “Dynamics of solitons in the model of nonlinear Schrödinger equation with an external harmonic potential,” IEEE J. Quantum Electron. 35, 778-786 (2005).
[CrossRef]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable ring-profile vortex solitons in Bessel optical lattices,” Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Topological dragging of solitons,” Phys. Rev. Lett. 95, 243902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, “Spatial soliton switching in quasi-continuous optical arrays,” Opt. Lett. 24, 766-768 (2004).
[CrossRef]

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

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton trains in photonic lattices,” Opt. Express 12, 2831-2837 (2004).
[CrossRef] [PubMed]

Wang, H.

Winternitz, P.

C. R. Menyuk, D. Levi, and P. Winternitz, “Self-similarity in transient stimulated Raman scattering,” Phys. Rev. Lett. 69, 3048-3051 (1992).
[CrossRef] [PubMed]

Wise, F. W.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Xie, R. H.

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

Xu, J. J.

Z. Chen, H. Martin, E. D. Eugenieva, J. J. Xu, and A. Bezryadina1, “Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains,” Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

Yang, J.

Yang, X.

Yi, L.

J. Liang, H. Liu, F. Liu, and L. Yi, “Analytical solutions to the fully extended nonlinear Schrödinger equation,” J. Phys. A: Math. Theor. 42, 335204 (2009).
[CrossRef]

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

W. P. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75, 061801 (2007).
[CrossRef]

S. H. Chen and L. Yi, “Self-similar evolutions of parabolic, Hermite-Gaussian, and hybrid optical pulses: Universality and diversity,” Phys. Rev. E 72, 016622 (2005).
[CrossRef]

S. H. Chen, L. Yi, D. S. Guo, and P. X. Lu, “Chirped self-similar solutions of a generalized nonlinear Schrödinger equation model,” Phys. Rev. E 71, 016606 (2005).
[CrossRef]

Zelenina, A. S.

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, “Spatial soliton switching in quasi-continuous optical arrays,” Opt. Lett. 24, 766-768 (2004).
[CrossRef]

Zentgraf, T.

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

Zhong, W. P.

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

W. P. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75, 061801 (2007).
[CrossRef]

Zhou, W.

Ziad, H.

IEEE J. Quantum Electron. (1)

C. H. Tenorio, E. V. Vargas, V. N. Serkin, M. A. Granados, T. L. Belyaeva, R. P. Moreno, and L. M. Lara, “Dynamics of solitons in the model of nonlinear Schrödinger equation with an external harmonic potential,” IEEE J. Quantum Electron. 35, 778-786 (2005).
[CrossRef]

J. Opt. Soc. Am. B (2)

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

J. Liang, H. Liu, F. Liu, and L. Yi, “Analytical solutions to the fully extended nonlinear Schrödinger equation,” J. Phys. A: Math. Theor. 42, 335204 (2009).
[CrossRef]

J. Phys. B (1)

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

Opt. Express (3)

Opt. Lett. (7)

Phys. Rev. A (1)

W. P. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75, 061801 (2007).
[CrossRef]

Phys. Rev. E (4)

S. H. Chen, L. Yi, D. S. Guo, and P. X. Lu, “Chirped self-similar solutions of a generalized nonlinear Schrödinger equation model,” Phys. Rev. E 71, 016606 (2005).
[CrossRef]

S. H. Chen and L. Yi, “Self-similar evolutions of parabolic, Hermite-Gaussian, and hybrid optical pulses: Universality and diversity,” Phys. Rev. E 72, 016622 (2005).
[CrossRef]

M. Soljacic, M. Segev, and C. R. Menyuk, “Self-similarity and fractals in soliton-supporting systems,” Phys. Rev. E 61, R1048-R1051 (2000).
[CrossRef]

B. A. Malomed and P. G. Kevrekidis, “Discrete vortex solitons,” Phys. Rev. E 64, 026601 (2001).
[CrossRef]

Phys. Rev. Lett. (17)

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90, 113902 (2003).
[CrossRef] [PubMed]

V. N. Serkin and A. Hasegawa, “Novel soliton solutions of the nonlinear Schrödinger equation model,” Phys. Rev. Lett. 85, 4502-4505 (2000).
[CrossRef] [PubMed]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010-6013 (2000).
[CrossRef] [PubMed]

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

C. R. Menyuk, D. Levi, and P. Winternitz, “Self-similarity in transient stimulated Raman scattering,” Phys. Rev. Lett. 69, 3048-3051 (1992).
[CrossRef] [PubMed]

S. A. Ponomarenko and G. P. Agrawal, “Do solitonlike self-similar waves exist in nonlinear optical media?” Phys. Rev. Lett. 97, 013901 (2006).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, and J. S. Aitchison, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett. 83, 2726-2729 (1999).
[CrossRef]

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

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

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

Z. Chen, H. Martin, E. D. Eugenieva, J. J. Xu, and A. Bezryadina1, “Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains,” Phys. Rev. Lett. 92, 143902 (2004).
[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, 213906-213909 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable ring-profile vortex solitons in Bessel optical lattices,” Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[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, 023902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Topological dragging of solitons,” Phys. Rev. Lett. 95, 243902 (2005).
[CrossRef] [PubMed]

Other (4)

A. M. Glass and J. Strait, “The photorefractive effect in semiconductors,” in Photorefractive Materials and their Applications I, P.Gunter and J.P.Huignard, eds. (Springer, 1988), p. 237(R)C262.

V. I. Karpman, Non-Linear Waves in Dispersive Media (Pergamon, 1975).

S. M. Richardson, Fluid Mechanics (Hemisphere Publishing Corp., 1989).

G. I. Barenblatt, Scaling, Self-Similarity, and Intermediate Asymptotics (Cambridge Univ. Press, 1996).

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Figures (7)

Fig. 1
Fig. 1

Amplitude comparison of radial distribution of J m solitons, corresponding to J 0 , J 1 , J 2 , J 3 from top to bottom.

Fig. 2
Fig. 2

Soliton clusters of the BSL01 beam at z = 0 in lossless media. (a) Intensity distribution. (b) The contour plots in the x y plane. In our calculations, the following parameters are used: a 0 = c 0 = P 0 = q = r 0 = 1 , β 0 = α = 0.01 , σ = 0.01 , m = g ( z ) = 0 .

Fig. 3
Fig. 3

Amplitude comparison of analytical solutions with numerical simulations to Eq. (1) for various distances z = 0 , 10 , 20 , 30 from left to right. Analytical solutions (top row), numerical simulations (middle row), with a white noise of variance σ 2 = 0.05 (bottom row). The other coefficients are the same as in Fig. 2.

Fig. 4
Fig. 4

Intensity of BSL03, BSL13, BSL23, and BSL33 solitons from left to right for z = 5 , q = 1 (top row) and the contour plots (low row). The others are the same as in Fig. 2.

Fig. 5
Fig. 5

Contours of BSL03, BSL13, BSL23, and BSL33 solitons from left to right for q = 0.5 (top row) and q = 0.2 (low row) at the fixed z = 5 . The others are the same as in Fig. 2.

Fig. 6
Fig. 6

Intensity of BSL21, BSL22, BSL23, and BSL24 solitons from left to right (top row) for z = 5 and q = 0.5 . The contours are plotted. The others are the same as in Fig. 2.

Fig. 7
Fig. 7

Intensity of BSL m n solitons on the top row n = 2 , and bottom row, n = 5 , for q = 0 , z = 5 . From left to right, one takes m = 3 , 4 , 5 , 6 . The others are the same as in Fig. 2.

Equations (21)

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

i ψ z = β ( z ) 2 2 ψ γ ( z ) | ψ | 2 ψ + p ( z ) R ( r , φ , z ) ψ + i g ( z ) 2 ψ ,
A A z + β ( z ) 2 [ 2 A r 2 A ( A r ) 2 + 1 r A r + 1 r 2 2 A φ 2 A r 2 ( B φ ) 2 ] γ ( z ) A 3 + p R A = 0 ,
A z β ( z ) 2 ( 2 A z B z + A 2 B r 2 + A r B r + 2 r 2 A φ B φ + A r 2 2 B φ 2 ) g ( z ) 2 A = 0 .
A ( z , r , φ ) = k P ( z ) Φ ( φ ) w ( z ) F ( θ ) ,
B ( z , r ) = a ( z ) + c ( z ) ( r r c ) 2 ,
c ( z ) = c 0 1 c 0 D ( z ) .
θ 2 d 2 F ( θ ) d θ 2 + θ d F ( θ ) d θ + { 2 [ 1 c 0 D ( z ) ] 2 β ( z ) d a ( z ) d z θ 2 + 1 Φ ( φ ) d 2 Φ ( φ ) d φ 2 } F ( θ ) + Π ( z , r , φ ) = 0 ,
1 Φ ( φ ) d 2 Φ ( φ ) d φ 2 = m 2
2 [ 1 c 0 D ( z ) ] 2 β ( z ) d a ( z ) d z = λ 2 .
Φ ( φ ) = 1 1 + q 2 [ cos ( m φ ) + i q sin ( m φ ) ]
a ( z ) = a 0 + λ 2 2 0 z β ( z ) [ 1 c 0 D ( z ) ] 2 d z ,
θ 2 d 2 F ( θ ) d θ 2 + θ d F ( θ ) d θ + ( λ 2 θ 2 m 2 ) F ( θ ) + Π ( r , φ , z ) = 0 .
d 2 F ( θ ) d θ 2 + 1 θ d F ( θ ) d θ + [ λ 2 m 2 θ 2 ] F ( θ ) = 0 .
ψ ( r , φ , z ) = 2 P r 0 w ( z ) J ( m + 1 ) n ( μ n m ) J m n ( μ n m w ( z ) r r 0 ) Φ ( φ ) e i [ a ( z ) + c ( z ) r 2 ] .
β ( z ) = β 0 e σ z , γ ( z ) = γ 0 e α z .
G ( z ) = 0 z g ( z ) d z = ( α + σ ) z
ω ( z ) = 1 + 2 c 0 β 0 σ ( e σ z 1 ) .
ψ ( r , φ , z ) = Ω ( z ) J m n ( μ n m r 0 w ( z ) r ) [ cos ( m φ ) + i q sin ( m φ ) ] e ( α + σ ) z 2 + i [ a ( z ) + c ( z ) r 2 ] ,
a ( z ) = a 0 + λ 2 σ 4 c 0 [ 1 ( σ 2 c 0 β 0 ) + 2 c 0 β 0 e σ z 1 σ ]
c ( z ) = c 0 1 c 0 D ( z ) = c 0 σ ( σ 2 c 0 β 0 ) + 2 c 0 β 0 e σ z ,
| Φ | 2 = 1 1 + q 2 [ 1 + ( q 2 1 ) sin 2 ( m φ ) ] .

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