Some Further Results on Traveling Wave Solutions for the ZK‐BBM(m, n) Equations

Shaoyong Li and Zhengrong Liu

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

Abstract: We investigate the traveling wave solutions for the ZK‐BBM(m, n) equations ut+ux-aumx+bunxt+kunytx=0 by using bifurcation method of dynamical systems. Firstly, for ZK‐BBM(2, 2) equation, we obtain peakon wave, periodic peakon wave, and smooth periodic wave solutions and point out that the peakon wave is the limit form of the periodic peakon wave. Secondly, for ZK‐BBM(3, 2) equation, we obtain some elliptic function solutions which include periodic blow‐up and periodic wave. Furthermore, from the limit forms of the elliptic function solutions, we obtain some trigonometric and hyperbolic function solutions which include periodic blow‐up, blow‐up, and smooth solitary wave. We also show that our work extends some previous results.

Date: 2013
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https://doi.org/10.1155/2013/156139

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:156139

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