J4 ›› 2010, Vol. 45 ›› Issue (4): 100-105.

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A generalized [G′/G]expansion method and its applications in nonlinear mathematical physics equations

 LV Hai-Ling, LIU Xi-Qiang, NIU Lei   

  1. School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, Shandong, China
  • Received:2009-06-07 Online:2010-04-10 Published:2010-05-19
  • About author:Lv Hai-ling(1983-),female,postgraduate,major in the exact solutions of nonlinear evolution equations.Email:lvhailing20090908@126.com
  • Supported by:

    Supported by the Natural Science Foundation of Shandong Province in China (Y 2008A 35 and Y 2007G 64)

Abstract:

A generalized [G′/G]-expansion method is proposed by studying Wang′s [G′/G]-expansionmethod and the  first order nonlinear ordinary differential equation with a sixth-order nonlinear term. The method is applied to (2+1)-dimensional dispersive long wave equations and double sineGordon equation. As a result, some new exact travelling wave solutions are obtained which include solitary wave solutions, triangular periodic wave solutions, hyperbolic solutions, rational solutions and Jacobi elliptic doubly periodic wave solutions. This method can also be applied to other nonlinear evolution equations in mathematical physics.

Key words:  generalized[ G′/G]expansion method; dispersive long wave equations; double sine-Gordon equation; travelling wave solution

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