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Periodic wave solutions and their limits for the ZK–BBM equation

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  • Song, Ming
  • Liu, Zhengrong

Abstract

In this paper, we use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the ZK–BBM equation. Some explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain solitary wave solutions, periodic wave solutions, kink wave solutions, unbounded solutions and blow-up wave solutions.

Suggested Citation

  • Song, Ming & Liu, Zhengrong, 2014. "Periodic wave solutions and their limits for the ZK–BBM equation," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 9-26.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:9-26
    DOI: 10.1016/j.amc.2014.01.048
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    References listed on IDEAS

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    1. Ming Song, 2012. "Application of Bifurcation Method to the Generalized Zakharov Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-8, November.
    2. Ming Song & Shaoyong Li & Jun Cao, 2010. "New Exact Solutions for the -Dimensional Broer-Kaup-Kupershmidt Equations," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-9, December.
    3. Shen, Jianwei & Xu, Wei, 2005. "Bifurcations of smooth and non-smooth travelling wave solutions in the generalized Camassa–Holm equation," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1149-1162.
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