A unified approach in seeking the solitary wave solutions to sine–Gordon type equations

Abstract

By utilizing the solutions of an auxiliary ordinary differential equation introduced in this paper, we present a simple and direct method to uniformly construct the exact solitary wave solutions for sine–Gordon type equations. As illustrative examples, the exact solitary wave solutions of some physically significant sine–Gordon type equations, including the sine–Gordon equation, double sine–Gordon equation and mKdV–sine–Gordon equation, are investigated by means of this method.