Stable Optical Solitons for the Higher-Order Non-Kerr NLSE via the Modified Simple Equation Method

This paper studies the propagation of the short pulse optics model governed by the higher-order nonlinear Schrödinger equation (NLSE) with non-Kerr nonlinearity. Exact one-soliton solutions are derived for a generalized case of the NLSE with the aid of software symbolic computations. The modified Kudryashov simple equation method (MSEM) is employed for this purpose under some parametric constraints. The computational work shows the difference, effectiveness, reliability, and power of the considered scheme. This method can treat several complex higher-order NLSEs that arise in mathematical physics. Graphical illustrations of some obtained solitons are presented.

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Soliton solutions of perturbed nonlinear Schrodinger equation with Kerr law nonlinearity via the modified simple equation method and the subordinary differential equation method

TURKISH JOURNAL OF PHYSICS ◽

10.3906/fiz-1803-18 ◽

2018 ◽

Vol 42 (4) ◽

pp. 425-432

Author(s):

Singh Subhaschandra SALAM

Keyword(s):

Differential Equation ◽

Schrodinger Equation ◽

Soliton Solutions ◽

Nonlinear Schrodinger Equation ◽

Simple Equation ◽

Equation Method ◽

Kerr Law ◽

Kerr Law Nonlinearity ◽

Modified Simple Equation Method ◽

Differential Equation Method

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New Soliton Solutions of the (2+1)-Dimensional System Davey-Stewartson Equation

International Journal of Engineering & Technology ◽

10.14419/ijet.v7i4.1.19489 ◽

2018 ◽

Vol 7 (4.1) ◽

pp. 37 ◽

Cited By ~ 1

Author(s):

Anwar J Ja'afar Mohamad Jawad ◽

Mahmood J. Abu-Al Shaeer ◽

Marko D. Petkovi_c

Keyword(s):

Soliton Solutions ◽

Travelling Wave ◽

Simple Equation ◽

Equation Method ◽

Initial System ◽

Wave Transformation ◽

Dimensional System ◽

Modified Simple Equation Method ◽

Complex Coefficients

In this paper, we derive several soliton solutions of the generalized Davey-Stewartson equation with the complex coefficients. First we use the travelling wave transformation to reduce the initial system to ODE. The equivalent ODE is then solved, giving several classes of solutions, depending on the values of the parameters. Finally, the Extended Tanh-Coth method and Modified simple equation method.

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The Modified Simple Equation Method, the Exp-Function Method, and the Method of Soliton Ansatz for Solving the Long–Short Wave Resonance Equations

Zeitschrift für Naturforschung A ◽

10.1515/zna-2015-0414 ◽

2016 ◽

Vol 71 (2) ◽

pp. 103-112 ◽

Cited By ~ 20

Author(s):

E.M.E. Zayed ◽

Abdul-Ghani Al-Nowehy

Keyword(s):

Exact Solutions ◽

Function Method ◽

Nonlinear Partial Differential Equations ◽

Soliton Solutions ◽

Dark Soliton ◽

Short Wave ◽

Simple Equation ◽

Equation Method ◽

Wave Resonance ◽

Modified Simple Equation Method

AbstractThe modified simple equation method, the exp-function method, and the method of soliton ansatz for solving nonlinear partial differential equations are presented. Based on these three different methods, we obtain the exact solutions and the bright–dark soliton solutions with parameters of the long-short wave resonance equations which describe the resonance interaction between the long wave and the short wave. When these parameters take special values, the solitary wave solutions are derived from the exact solutions. We compare the results obtained using the three methods. Also, a comparison between our results and the well-known results is given.

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