The Traveling Wave Solutions and Their Bifurcations for the BBM‐Like B(m, n) Equations

Shaoyong Li and Zhengrong Liu

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

Abstract: We investigate the traveling wave solutions and their bifurcations for the BBM‐like B(m, n) equations ut+αux+β(um)x−γ(un)xxt=0 by using bifurcation method and numerical simulation approach of dynamical systems. Firstly, for BBM‐like B(3, 2) equation, we obtain some precise expressions of traveling wave solutions, which include periodic blow‐up and periodic wave solution, peakon and periodic peakon wave solution, and solitary wave and blow‐up solution. Furthermore, we reveal the relationships among these solutions theoretically. Secondly, for BBM‐like B(4, 2) equation, we construct two periodic wave solutions and two blow‐up solutions. In order to confirm the correctness of these solutions, we also check them by software Mathematica.

Date: 2013
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https://doi.org/10.1155/2013/490341

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:490341

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