Study of abundant explicit wave solutions of the Drinfeld-Sokolov-Satsuma-Hirota (DSSH) equation and the shallow water wave equation

Abstract

In this article, the two variable (G′/G,1/G)-expansion method is suggested to investigate new and further general multiple exact wave solutions to the Drinfeld-Sokolov-Satsuma-Hirota (DSSH) equation and the shallow water wave equation which arise in mathematical physics with the aid of computer algebra software, like Mathematica. Three types of traveling wave solutions, videlicet the hyperbolic functions, the trigonometric functions and the rational functions solution are found. The method demonstrates power, reliability and efficiency. Indeed, the method is the generalization of the well-known (G′/G)-expansion method established by Wang et al. and the method also presents a wider applicability for conducting nonlinear wave equations.