The Traveling Wave Solutions and Their Bifurcations for the BBM-Like Equations

Shaoyong Li and Zhengrong Liu

Journal of Applied Mathematics, 2013, vol. 2013, 1-17

Abstract:

We investigate the traveling wave solutions and their bifurcations for the BBM-like equations by using bifurcation method and numerical simulation approach of dynamical systems. Firstly, for BBM-like 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 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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:490341

DOI: 10.1155/2013/490341

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