Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (7): 788-793.

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NEW EXPLICIT AND EXACT TRAVELLING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR EVOLUTION EQUATIONS

XIA Tie-cheng, ZHANG Hong-qing, YAN Zhen-ya   

  1. Department of Mathematics, Dalian University of Technology, Dalian 116024, P. R. China
  • Received:2000-05-08 Revised:2001-03-23 Online:2001-07-18 Published:2001-07-18
  • Supported by:
    the National Key Basic Research Development Project of China(1998030600);the National Natural Science Foundation of China(10072013);the Doctoral Program Foundation of Institution of Higher Education of China(98014119)

Abstract: With the help of Mathematica, many travelling for a class of nonlinear evolution equations utt+auxx+bu+cu2+du3=0 are obtained by using hyperbola function method and WU-elimation method, which include new travelling wave solutions, periodic solutions and kink soliton solutions. Some equations such as Duffing equation, sin-Gordon equation, 4 and Klein-Gordon equation are particular cases of the evolution equations. The method can also be applied to other nonlinear equations.

2010 MSC Number: 

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