Abstract
In this paper, we explore the travelling wave solutions for some nonlinear partial differential equations by using the recently established rational (G' /G)-expansion method. We apply this method to the combined KdV-mKdV equation, the reaction-diffusion equation and the coupled Hirota-Satsuma KdV equations. The travelling wave solutions are expressed by hyperbolic functions, trigonometric functions and rational functions. When the parameters are taken as special values, the solitary waves are also derived from the travelling waves. We have also given some figures for the solutions.
Highlights
In the past decades, the travelling wave solutions of nonlinear partial differential equations (NLPDEs) play an effective role in physics, engineering and applied mathematics
We explore the travelling wave solutions for some nonlinear partial differential equations by using the recently established rational (G′/G)-expansion method
We have obtained various types of travelling wave solutions for the combined KdV-mKdV equation, the reaction-diffusion equation, and the coupled Hirota-Satsuma KdV equations that are solved by using the rational (G′/G)expansion method
Summary
The travelling wave solutions of nonlinear partial differential equations (NLPDEs) play an effective role in physics, engineering and applied mathematics. Many researchers have been proposed various different methods to find solutions for nonlinear partial differential equations and nonlinear fractional differential equations [36,37,38,39,40]. The rational (G′/G)-expansion method, travelling wave solution, the combined KdV-mKdV equation, the reaction-diffusion equation, the coupled Hirota-Satsuma KdV equations. Wang et al [16] first introduced the (G′/G)-expansion method to find travelling wave solutions of nonlinear evolution equations. In this paper we use the rational (G′/G)- expansion method and apply for the combined KdV-mKdV equation, the reaction-diffusion equation, and the coupled Hirota-Satsuma KdV equations. We derived abundant solutions for each equation that is different from the solutions in the literature
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