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By using the self-similar method to solve the nonlinear Schrödinger eguation with distributed coefficients, the self-similar solitons in Bessel lattice are studied under the hollow cylinder boundary conditions and the analytical solutions are obtained. Analytical solutions and numerical solutions are found to be identical. The result indicates that optical lattices induced by non-diffractive Bessel beams are possible to support stable self-similar soliton clusters.
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Keywords:
- spatial optical solitons /
- Bessel lattice /
- boundary /
- self-similarity
[1] Fleischer J W, Segev M, Efremidis N, Christodoulides D N 2003 Nature (London) 422 147
[2] Efremidis N K, Hudock J, Christodoulides D N, Fleischer J W, Cohen O, Segev M 2003 Phys. Rev. Lett. 91 213906
[3] Kartashov Y V, Vysloukh V A, Torner L 2004 Opt. Expres 12 2831
[4] Neshev D, Ostrovskaya E, Kivshar Y, Krolikowski W 2003 Opt. Lett. 28 710
[5] Chen S M, Shi S X, Dong H Z 2007 Acta Phys. Sin. 56 1379 (in Chinese) [陈守满, 石顺祥, 董洪舟 2007 56 1379]
[6] Qing X J, Shao Y Q, Guo Q 2007 Acta Phys. Sin. 56 5269 (in Chinese) [秦晓娟, 邵毅全, 郭旗 2007 56 5269]
[7] Liang J C, Liu H, Liu F, Yi L, 2009 J. Phys. A Math. Theor. 42 335204
[8] Liang J C, Cai Z B, Yi L, Wang H C, 2010 Opt. Commun. 283 386
[9] Song X, Li H M 2013 Phys. Lett. A 377 714
[10] He J R, Li H M, Li L 2012 Phys. Lett. A 376 3108
[11] Ablowitz M J 1991 Nonlinear Schrödinger Equation and Inverse Scattering. (New York: Cambridge University Press)
[12] Matveev V B, Salle M A 1991 Dardoux Transformations and Solitons (Berlin: Springer Series in Non-linear Dynamics)
[13] Kruglov V I, Peacock A C, Harvey J D 2003 Phys. Rev. Lett. 90 113902
[14] Zhang S W, Yi L 2008 Phys. Rev. E 78 026602
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[1] Fleischer J W, Segev M, Efremidis N, Christodoulides D N 2003 Nature (London) 422 147
[2] Efremidis N K, Hudock J, Christodoulides D N, Fleischer J W, Cohen O, Segev M 2003 Phys. Rev. Lett. 91 213906
[3] Kartashov Y V, Vysloukh V A, Torner L 2004 Opt. Expres 12 2831
[4] Neshev D, Ostrovskaya E, Kivshar Y, Krolikowski W 2003 Opt. Lett. 28 710
[5] Chen S M, Shi S X, Dong H Z 2007 Acta Phys. Sin. 56 1379 (in Chinese) [陈守满, 石顺祥, 董洪舟 2007 56 1379]
[6] Qing X J, Shao Y Q, Guo Q 2007 Acta Phys. Sin. 56 5269 (in Chinese) [秦晓娟, 邵毅全, 郭旗 2007 56 5269]
[7] Liang J C, Liu H, Liu F, Yi L, 2009 J. Phys. A Math. Theor. 42 335204
[8] Liang J C, Cai Z B, Yi L, Wang H C, 2010 Opt. Commun. 283 386
[9] Song X, Li H M 2013 Phys. Lett. A 377 714
[10] He J R, Li H M, Li L 2012 Phys. Lett. A 376 3108
[11] Ablowitz M J 1991 Nonlinear Schrödinger Equation and Inverse Scattering. (New York: Cambridge University Press)
[12] Matveev V B, Salle M A 1991 Dardoux Transformations and Solitons (Berlin: Springer Series in Non-linear Dynamics)
[13] Kruglov V I, Peacock A C, Harvey J D 2003 Phys. Rev. Lett. 90 113902
[14] Zhang S W, Yi L 2008 Phys. Rev. E 78 026602
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