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Peaked and Smooth Solitons for K*(4,1) Equation

Author

Listed:
  • Yongan Xie
  • Hualiang Fu
  • Shengqiang Tang

Abstract

This paper is contributed to explore all possible single peak solutions for the K*(4,1) equation ut = uxu2 + 2α(uuxxx + 2uxuxx). Our procedure shows that the K*(4,1) equation either has peakon, cuspon, and smooth soliton solutions when sitting on a nonzero constant pedestal limξ→±∞u = A ≠ 0 or possesses compacton solutions only when limξ→±∞u = A = 0. We present a new smooth soliton solution in an explicit form. Mathematical analysis and numeric graphs are provided for those soliton solutions of the K*(4,1) equation.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:518415
    DOI: 10.1155/2013/518415
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    References listed on IDEAS

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    1. Hasibun Naher & Farah Aini Abdullah, 2012. "New Traveling Wave Solutions by the Extended Generalized Riccati Equation Mapping Method of the (2 + 1)‐Dimensional Evolution Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Hasibun Naher & Farah Aini Abdullah & M. Ali Akbar, 2012. "New Traveling Wave Solutions of the Higher Dimensional Nonlinear Partial Differential Equation by the Exp‐Function Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Hasibun Naher & Farah Aini Abdullah & M. Ali Akbar, 2012. "New Traveling Wave Solutions of the Higher Dimensional Nonlinear Partial Differential Equation by the Exp-Function Method," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, January.
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    Cited by:

    1. 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).

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