The (ω/ g )-expansion method and its application to Vakhnenko equation

This paper presents a new function expansion method for finding travelling wave solutions of a nonlinear evolution equation and calls it the (ω/ g )-expansion method, which can be thought of as the generalization of ( G '/ G )-expansion given by Wang et al recently. As an application of this new method, we study the well-known Vakhnenko equation which describes the propagation of high-frequency waves in a relaxing medium. With two new expansions, general types of soliton solutions and periodic solutions for Vakhnenko equation are obtained.