New application of (G′/G)(G′/G)-expansion method to a nonlinear evolution equation

A series of exact traveling wave solutions are constructed by applying the (G′/G)(G′/G)-expansion method for a modified generalized Vakhnenko equation. A further investigation shows that the shape types of the solitary wave solutions could directly depend on the coefficients of the linear ordinary differential equation with the (G′/G)(G′/G)-expansion method. Hump-like solitary wave solution, cusp-like solitary wave solution and loop-like solitary wave solution can be observed by setting the coefficients at different values.