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

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  • Shaoyong Li
  • Zhengrong Liu

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.

Suggested Citation

  • Shaoyong Li & Zhengrong Liu, 2013. "The Traveling Wave Solutions and Their Bifurcations for the BBM‐Like B(m, n) Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:490341
    DOI: 10.1155/2013/490341
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    References listed on IDEAS

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    1. Abdou, M.A., 2007. "The extended F-expansion method and its application for a class of nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 95-104.
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    Cited by:

    1. Zhenshu Wen, 2014. "New Exact Explicit Nonlinear Wave Solutions for the Broer‐Kaup Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).

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