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Elliptic equation rational expansion method and new exact travelling solutions for Whitham–Broer–Kaup equations

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  • Chen, Yong
  • Wang, Qi
  • Li, Biao

Abstract

Based on a new general ansatz and a general subepuation, a new general algebraic method named elliptic equation rational expansion method is devised for constructing multiple travelling wave solutions in terms of rational special function for nonlinear evolution equations (NEEs). We apply the proposed method to solve Whitham–Broer–Kaup equation and explicitly construct a series of exact solutions which include rational form solitary wave solution, rational form triangular periodic wave solutions and rational wave solutions as special cases. In addition, the links among our proposed method with the method by Fan [Chaos, Solitons & Fractals 2004;20:609], are also clarified generally.

Suggested Citation

  • Chen, Yong & Wang, Qi & Li, Biao, 2005. "Elliptic equation rational expansion method and new exact travelling solutions for Whitham–Broer–Kaup equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 231-246.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:1:p:231-246
    DOI: 10.1016/j.chaos.2004.12.020
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    Cited by:

    1. Wang, Deng-Shan & Li, Hong-Bo & Wang, Jike, 2008. "The novel solutions of auxiliary equation and their application to the (2+1)-dimensional Burgers equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 374-382.

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