zbMATH — the first resource for mathematics

The simplest equation method to study perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity. (English) Zbl 1245.35121
Summary: The simplest equation method is a powerful solution method for obtaining exact solutions of nonlinear evolution equations.
In this paper, the simplest equation method is used to construct exact solutions of nonlinear Schrödinger’s equation and perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity. It is shown that the proposed method is effective and general.

35Q55 NLS equations (nonlinear Schrödinger equations)
35G20 Nonlinear higher-order PDEs
Full Text: DOI
[1] Ablowitz, M.J.; Segur, H., Solitons and inverse scattering transform, (1981), SIAM Philadelphia · Zbl 0472.35002
[2] Kudryashov, N.A., Exact solitary waves of the Fisher equation, Phys lett A, 342, 1-2, 99-106, (2005) · Zbl 1222.35054
[3] Kudryashov, N.A., Simplest equation method to look for exact solutions of nonlinear differential equations, Chaos soliton fract, 24, 5, 1217-1231, (2005) · Zbl 1069.35018
[4] Ma, W.X., Travelling wave solutions to a seventh order generalized KdV equation, Phys lett A, 180, 221-224, (1993)
[5] Malfliet, W., Solitary wave solutions of nonlinear wave equations, Amer J phys, 60, 7, 650-654, (1992) · Zbl 1219.35246
[6] Ma, W.X.; Huang, T.W.; Zhang, Y., A multiple exp-function method for nonlinear differential equations and its application, Phys scr, 82, 065003, (2010) · Zbl 1219.35209
[7] Miura, M.R., Backlund transformation, (1978), Springer-Verlag Berlin
[8] Hirota, R., Exact solution of the korteweg – de Vries equation for multiple collision of solitons, Phys rev lett, 27, 1192-1194, (1971) · Zbl 1168.35423
[9] Hirota, R., The direct method in soliton theory, (2004), Cambridge University Press
[10] Ma, W.X.; Lee, J.-H., A transformed rational function method and exact solutions to the (3+1)-dimensional jimbo – miwa equation, Chaos solitons fract, 42, 1356-1363, (2009) · Zbl 1198.35231
[11] Vitanov, N.K.; Dimitrova, Z.I., Application of the method of simplest equation for obtaining exact traveling-wave solutions for two classes of model PDEs from ecology and population dynamics, Commun nonlinear sci numer simul, 15, 10, 2836-2845, (2010) · Zbl 1222.35201
[12] Vitanov, N.K.; Dimitrova, Z.I.; Kantz, H., Modified method of simplest equation and its application to nonlinear pdes, Appl math comput, 216, 9, 2587-2595, (2010) · Zbl 1195.35272
[13] Zhang, Z.Y.; Liu, Z.H.; Miao, X.J.; Chen, Y.Z., New exact solutions to the perturbed nonlinear schrödinger’s equation with Kerr law nonlinearity, Appl math comput, 216, 3064-3072, (2010) · Zbl 1195.35283
[14] Biswas, A.; Konar, S., Introduction to non-Kerr law optical solitons, (2007), CRC Press Boca Raton, FL, USA · Zbl 1156.78001
[15] Biswas, A., Quasi-stationary non-Kerr law optical solitons, Opt fiber technol, 9, 4, 224-259, (2003)
[16] Özis, T.; Yildirim, A., Reliable analysis for obtaining exact soliton solutions of nonlinear Schrödinger (NLS) equation, Chaos solitons fract, 38, 209-212, (2008) · Zbl 1142.35605
[17] Kohl, R.; Biswas, A.; Milovic, D.; Zerrad, E., Optical soliton perturbation in a non-Kerr law media, Opt laser technol, 40, 4, 647-662, (2008)
[18] Biswas, A.; Fessak, M.; Johnson, S.; Beatrice, S.; Milovic, D.; Jovanoski, Z.; Kohl, R.; Majid, F., Optical soliton perturbation in non-Kerr law media traveling wave solution, Opt laser technol, 44, 1, 263-268, (2012)
[19] Green, P.D.; Biswas, A., Bright and dark optical solitons with time-dependent coefficients in a non-Kerr law media, Commun nonlinear sci numer simul, 15, 12, 3865-3873, (2010) · Zbl 1222.78040
[20] Topkara, E.; Milovic, D.; Sarma, A.K.; Zerrad, E.; Biswas, A., Optical solitons with non-Kerr law nonlinearity and inter-modal dispersion with time-dependent coefficients, Commun nonlinear sci numer simul, 15, 9, 2320-2330, (2010) · Zbl 1222.78044
[21] Biswas, A.; Milovic, D., Bright and dark solitons of the generalized nonlinear schrödinger’s equation, Commun nonlinear sci numer simul, 15, 6, 1473-1484, (2010) · Zbl 1221.78033
[22] Ma, W.X.; Fuchssteiner, B., Explicit and exact solutions to a kolmogorov – petrovskii – piskunov equation, Int J non-linear mech, 31, 329-338, (1996) · Zbl 0863.35106
[23] Ma, W.X., Comment on the 3+1 dimensional kadomtsev – petviashvili equations, Commun nonlinear sci numer simul, 16, 2663-2666, (2011) · Zbl 1221.35353
[24] Ma, W.X.; Chen, M., Direct search for exact solutions to the nonlinear Schrödinger equation, Appl math comput, 215, 2835-2842, (2009) · Zbl 1180.65130
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.