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Peakon, Cuspon, Compacton, and Loop Solutions of a Three‐Dimensional 3DKP(3, 2) Equation with Nonlinear Dispersion

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  • Haixia Zhao
  • Lijing Qiao
  • Shengqiang Tang

Abstract

We study peakon, cuspon, compacton, and loop solutions for the three‐dimensional Kadomtsev‐Petviashvili equation (3DKP(3,2) equation) with nonlinear dispersion. Based on the method of dynamical systems, the 3DKP(3,2) equation is shown to have the parametric representations of the solitary wave solutions such as peakon, cuspon, compacton, and loop solutions. As a result, the conditions under which peakon, cuspon, compacton, and loop solutions appear are also given.

Suggested Citation

  • Haixia Zhao & Lijing Qiao & Shengqiang Tang, 2014. "Peakon, Cuspon, Compacton, and Loop Solutions of a Three‐Dimensional 3DKP(3, 2) Equation with Nonlinear Dispersion," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:934987
    DOI: 10.1155/2014/934987
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    References listed on IDEAS

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    1. Dai, Chaoqing & Zhu, Jiamin & Zhang, Jiefang, 2006. "New exact solutions to the mKdV equation with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 881-886.
    2. Yongan Xie & Hualiang Fu & Shengqiang Tang, 2013. "Peaked and Smooth Solitons for Equation," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-10, December.
    3. Yongan Xie & Hualiang Fu & Shengqiang Tang, 2013. "Peaked and Smooth Solitons for K*(4,1) Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    4. Zhang, Huiqun, 2006. "New exact solutions for the sinh-Gordon equation," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 489-496.
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