Abstract This paper presents a new function expansion method for finding travelling wave solutions of a nonlinear evolution equation and calls it the ($\omega/g$)-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.
Received: 15 January 2008
Revised: 09 July 2008
Accepted manuscript online:
Li Wen-An(李文安), Chen Hao(陈浩), and Zhang Guo-Cai(张国才) The ($\omega/g$)-expansion method and its application to Vakhnenko equation 2009 Chin. Phys. B 18 400
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