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

  • Received: 01 December 2004 Accepted: 29 June 2018 Published: 01 November 2005
  • MSC : 92D30.

  • 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.

    Citation: Jibin Li, Weigou Rui, Yao Long, Bin He. Travelling wave solutions for higher-order wave equations of KDV type (III)[J]. Mathematical Biosciences and Engineering, 2006, 3(1): 125-135. doi: 10.3934/mbe.2006.3.125

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  • 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.


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