Application of the rational (G' /G)-expansion method for solving some coupled and combined wave equations

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.