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New explicit periodic wave solutions and their limits for modified form of Camassa-holm equation

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Abstract

In this paper, we consider the following nonlinear equation

$$ u_t + 2ku_x - u_{xxt} + au^2 u_x = 2u_x u_{xx} + uu_{xxx} , $$

which is a modified form of the Camassa-Holm equation. We construct four new explicit periodic wave solutions by bifurcation method of dynamical systems. We also obtain two explicit solitary wave solutions via the limits of the explicit periodic wave solutions. One of the two solitary wave solutions is new.

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Authors and Affiliations

  1. Department of Mathematics, South China University of Technology, Guangzhou, 510640, China

    Quan-di Wang & Min-ying Tang

Authors
  1. Quan-di Wang
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  2. Min-ying Tang
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Correspondence to Min-ying Tang.

Additional information

Supported by the National Natural Science Foundation of China (No. 10871073) and Guangdong Province (No.07006552).

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Wang, Qd., Tang, My. New explicit periodic wave solutions and their limits for modified form of Camassa-holm equation. Acta Math. Appl. Sin. Engl. Ser. 26, 513–524 (2010). https://doi.org/10.1007/s10255-008-8013-1

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  • DOI: https://doi.org/10.1007/s10255-008-8013-1

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