New exact solutions to sinh–cosh-Gordon equation by using techniques based on projective Riccati equations

Abstract

In this paper we present some methods for solving nonlinear partial differential equations which are based on the idea of the projective Riccati equations. We show how to derive well-known methods such as Conte’s projective Riccati equation method, tanh–coth method, He’s exp-function method and a new method we called sn–ns method. We illustrate the effectiveness of the sn–ns method for the problem of finding new exact solutions to the combined sinh–cosh-Gordon equation with the aid of Maple 14 and Mathematica 7.