Modified simple equation method to the nonlinear Hirota Satsuma KdV system

Abstract

In this article, we use the modified simple equation method to construct the exact traveling wave solutions for some nonlinear PDE's in mathematical physics namely the coupled Hirota \u2013 Satsuma KdV equations and the generalized coupled Hirota \u2013 Satsuma KdV equations. Based on this formulation, solitary solutions can be easily obtained by using the proposed method. Some known solutions obtained by the tanh- coth method are recovered as special cases. The proposed method is direct and more powerful than the other methods.