Three different methods for new soliton solutions of the generalized NLS equation. (English) Zbl 1470.35308

Jawad, Anwar Ja’afar Mohamad

Abstr. Appl. Anal. 2017, Article ID 5137946, 8 p. (2017).

Summary: Three different methods are applied to construct new types of solutions of nonlinear evolution equations. First, the Csch method is used to carry out the solutions; then the Extended Tanh-Coth method and the modified simple equation method are used to obtain the soliton solutions. The effectiveness of these methods is demonstrated by applications to the RKL model, the generalized derivative NLS equation. The solitary wave solutions and trigonometric function solutions are obtained. The obtained solutions are very useful in the nonlinear pulse propagation through optical fibers.

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
35C08	Soliton solutions

References:

[1]	Radhakrishnan, R.; Kundu, A.; Lakshmanan, M., Coupled nonlinear Schrödinger equations with cubic-quintic nonlinearity: integrability and soliton interaction in non-Kerr media, Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 60, 3, 3314-3323, (1999)
[2]	Hong, W.-P., Optical solitary wave solutions for the higher order nonlinear Schrödinger equation with cubic-quintic non-Kerr terms, Optics Communications, 194, 1–3, 217-223, (2001)
[3]	Wang, M.; Li, X.; Zhang, J., Sub-ODE method and solitary wave solutions for higher order nonlinear Schrödinger equation, Physics Letters A, 363, 1-2, 96-101, (2007) · Zbl 1197.81129
[4]	Triki, H.; Taha, T. R., Exact analytic solitary wave solutions for the RKL model, Mathematics and Computers in Simulation, 80, 4, 849-854, (2009) · Zbl 1186.35210
[5]	van Saarloos, W.; Hohenberg, P. C., Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations, Physica D: Nonlinear Phenomena, 56, 4, 303-367, (1992) · Zbl 0763.35088
[6]	Kundu, A., Landau-Lifshitz and higher-order nonlinear systems gauge generated from nonlinear Schrödinger type equations, Journal of Mathematical Physics, 25, 12, 3433-3438, (1984)
[7]	Kundu, A., Exact solutions to higher-order nonlinear equations through gauge transformation, Physica D: Nonlinear Phenomena, 25, 1-3, 399-406, (1987) · Zbl 0612.76002
[8]	Ebadi, G.; Biswas, A., The (G′/G) method and 1-soliton solution of the Davey-Stewartson equation, Mathematical and Computer Modelling, 53, 5-6, 694-698, (2011) · Zbl 1217.35171
[9]	Ebadia, G.; Krishnanb, E. V., Manel Labidic, Essaid Zerradd and Anjan Biswas, Analytical and numerical solutions to the Davey–Stewartson equation with power-law nonlinearity, Waves in Random and Complex Media, 21, 4, 559-590, (November 2011)
[10]	Xu, G.-q., Extended auxiliary equation method and its applications to three generalized NLS equations, Abstract and Applied Analysis, 2014, (2014) · Zbl 1468.35188
[11]	Jawad, A. J. M.; Mirzazadeh, M.; Zhou, Q.; Biswas, A., Optical solitons with anti-cubic nonlinearity using three integration schemes, Superlattices and Microstructures, 105, 1-10, (2017)
[12]	Jawad, A. J. M.; Petkovic, M. D.; Biswas, A., Soliton solutions to a few coupled nonlinear wave equations by tanh method, Iranian Journal of Science & Technology, 37, 2, 109-115, (2013) · Zbl 1317.65213
[13]	Jawad, A. J. M., Tan Method for Solitary Wave Solutions for Nonlinear Evolution Equations, Proceedings of the International Arab conference of Mathematics in Jordon
[14]	Jawad, A. J. M.; Petković, M. D.; Biswas, A., Modified simple equation method for nonlinear evolution equations, Applied Mathematics and Computation, 217, 1, 869-877, (2010) · Zbl 1201.65119