A generalized (G′/G)(G′/G)-expansion method and its applications to nonlinear evolution equations

In this paper, a generalized (G′/G)(G′/G)-expansion method and its algorithm are proposed by studying Wang’s (G′/G)(G′/G)-expansion method and constructing a first order nonlinear ordinary differential equation with a third-degree nonlinear term. Being concise and straightforward, the method is applied to combined KdV–MKdV equation and coupled Jaulent–Miodek equation. As a result, some new exact travelling wave solutions are obtained which include solitary wave solutions, triangular periodic wave solutions, exponential solutions, complex travelling solutions and rational solutions. This method can also be applied to other nonlinear evolution equations in mathematical physics.