Abstract
AbstractIn this article, the two variables (G′/G,1/G)-expansion method is suggested to obtain abundant closed form wave solutions to the perturbed nonlinear Schrodinger equation and the cubic-quintic Ginzburg-Landau equation arising in the analysis of various problems in mathematical physics. The wave solutions are expressed in terms of hyperbolic function, the trigonometric function, and the rational functions. The method can be considered as the generalization of the familiar (G′/G)-expansion method established by Wang et al. The approach of this method is simple, standard, and computerized. It is also powerful, reliable, and effective.
Highlights
Investigations of exact wave solutions to nonlinear evolution equations (NLEEs) play the central role in the study the complicated tangible phenomena
We introduce and implement the two variables (G ∕G, 1∕G)-expansion method to the perturbed nonlinear Schrodinger equation in the form (Zhang, 2008)
Nineteen traveling wave solutions of the perturbed nonlinear Schrodinger equation and twenty new traveling wave solutions of the cubic-quintic Ginzburg-Landau equation have been successfully obtained by using the G ∕G, 1∕G expansion method
Summary
Investigations of exact wave solutions to nonlinear evolution equations (NLEEs) play the central role in the study the complicated tangible phenomena. We introduce and implement the two variables (G ∕G, 1∕G)-expansion method to the perturbed nonlinear Schrodinger equation in the form (Zhang, 2008). In order to investigate exact traveling wave solutions of NLEEs by means of the two variables (G ∕G, 1∕G)-expansion method, the following steps need to be performed: Step 1: By means of the wave variable = x + y − v t, u(x, y, t) = u( ), Equation (2.7) can be reduced to an ODE as follows: P(u, −v u , u , v2 u , −v u , u ...) = 0.
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