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Travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation

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Abstract

The travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation u t −u xxt + (1+b)u m u x = bu x + uu xxx are considered where b > 1 and m are positive integers. The qualitative analysis methods of planar autonomous systems yield its phase portraits. Its soliton wave solutions, kink or antikink wave solutions, peakon wave solutions, compacton wave solutions, periodic wave solutions and periodic cusp wave solutions are obtained. Some numerical simulations of these solutions are also given.

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Authors and Affiliations

  1. Department of Mathematics, Zhanjiang Normal University, Zhanjiang, 524048, China

    ShengFu Deng

  2. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    BoLing Guo & TingChun Wang

  3. College of Math and Physics, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    TingChun Wang

Authors
  1. ShengFu Deng
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  2. BoLing Guo
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  3. TingChun Wang
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Correspondence to TingChun Wang.

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Deng, S., Guo, B. & Wang, T. Travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation. Sci. China Math. 54, 555–572 (2011). https://doi.org/10.1007/s11425-010-4122-4

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  • DOI: https://doi.org/10.1007/s11425-010-4122-4

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