The extended G′G-expansion method and its applications to the Whitham–Broer–Kaup–Like equations and coupled Hirota–Satsuma KdV equations

In this paper, based on a new general ansätze, the extended G′G-expansion method is proposed to seek exact solutions of nonlinear evolution equations. Being concise and straightforward, this method is applied to construct travelling wave solutions of Whitham–Broer–Kaup–Like equations and coupled Hirota–Satsuma KdV equations. By using this method, new exact solutions involving parameters, expressed by three types of functions which are the hyperbolic functions, the trigonometric functions and the rational functions, are obtained. When the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions.