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The extended Jacobi elliptic function method to solve a generalized Hirota–Satsuma coupled KdV equations

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  • Yu, Yaxuan
  • Wang, Qi
  • Zhang, Hongqing

Abstract

In this paper, we extend the Jacobi elliptic function rational expansion method by using a new generalized ansätz. With the help of symbolic computation, we construct more new explicit exact solutions of nonlinear evolution equations (NLEEs). We apply this method to a generalized Hirota–Satsuma coupled KdV equations and gain more general solutions. The general solutions not only contain the solutions by the existing Jacobi elliptic function expansion methods but also contain many new solutions. When the modulus of the Jacobi elliptic functions m→1 or 0, the corresponding solitary wave solutions and triangular functional (singly periodic) solutions are also obtained.

Suggested Citation

  • Yu, Yaxuan & Wang, Qi & Zhang, Hongqing, 2005. "The extended Jacobi elliptic function method to solve a generalized Hirota–Satsuma coupled KdV equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1415-1421.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:5:p:1415-1421
    DOI: 10.1016/j.chaos.2005.04.011
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    Cited by:

    1. Jang, Bongsoo, 2009. "New exact travelling wave solutions of nonlinear Klein–Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 646-654.
    2. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.

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