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Mathematical Biosciences and Engineering (MBE)
 

Travelling wave solutions for higher-order wave equations of KDV type (III)

Pages: 125 - 135, Volume 3, Issue 1, January 2006      doi:10.3934/mbe.2006.3.125

 
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Jibin Li - Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China (email)
Weigou Rui - Department of Mathematics, Honghe University, Mengzi, Yunnan 661100, China (email)
Yao Long - Department of Mathematics, Honghe University, Mengzi, Yunnan 661100, China (email)
Bin He - Department of Mathematics, Honghe University, Mengzi, Yunnan 661100, China (email)

Abstract: By using the theory of planar dynamical systems to the travelling wave equation of a higher order nonlinear wave equations of KdV type, the existence of smooth solitary wave, kink wave and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions are proved. In different regions of the parametric space, the sufficient conditions to guarantee the existence of the above solutions are given. In some conditions, exact explicit parametric representations of these waves are obtain.

Keywords:  travelling wave solutions, wave equation of KdV type.
Mathematics Subject Classification:  92D30.

Received: December 2004;      Accepted: March 2005;      Published: November 2005.