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

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.