中国物理B ›› 2009, Vol. 18 ›› Issue (2): 400-404.doi: 10.1088/1674-1056/18/2/004

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

李文安, 陈浩, 张国才   

  1. School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
  • 收稿日期:2008-01-15 修回日期:2008-07-09 出版日期:2009-02-20 发布日期:2009-02-20

The ($\omega/g$)-expansion method and its application to Vakhnenko equation

Li Wen-An(李文安), Chen Hao(陈浩)†, and Zhang Guo-Cai(张国才)   

  1. School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
  • Received:2008-01-15 Revised:2008-07-09 Online:2009-02-20 Published:2009-02-20

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摘要： 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.

关键词: (ω/g)-expansion method, Vakhnenko equation, travelling wave solutions

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.

Key words: ($\omega/g$)-expansion method, Vakhnenko equation, travelling wave solutions

中图分类号:  (Solitons)

  • 05.45.Yv
02.30.Jr (Partial differential equations)