Rational solitary wave solutions for some nonlinear differential difference equations

Abstract

In this article, we put a direct method to construct the rational solitary wave solutions for some nonlinear differential difference equations in mathematical physics which may be called the rational solitary wave difference method. We use the proposed method to construct the rational solitary exact solutions for some nonlinear differential difference equations via the lattice equation, the discrete nonlinear Klein Gordon equation. The proposed method is more effective and powerful to obtain many rational solitary exact solutions for nonlinear differential difference equations.