Multiple closed form wave solutions to the KdV and modified KdV equations through the rational (G′/G)-expansion method

Abstract

The purpose of this article is to generate the closed form traveling wave solutions of some nonlinear partial differential equations namely; the KdV equation and the modified KdV equation using the recently established rational (G′/G)-expansion method. By this method, new and further general closed form solutions expressed by three types of functions as for instance hyperbolic, trigonometric and rational function solutions are found. The basic ideas presented in this article and the obtained solutions might be useful to analyze the shallow water waves, ion acoustic waves in plasma, acoustic waves on a crystal lattice and the role of nonlinear dispersion in the formation of structures like liquid drops.