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Exact Traveling Wave Solutions of Explicit Type, Implicit Type, and Parametric Type for K(m, n) Equation

Author

Listed:
  • Xianbin Wu
  • Weiguo Rui
  • Xiaochun Hong

Abstract

By using the integral bifurcation method, we study the nonlinear K(m, n) equation for all possible values of m and n. Some new exact traveling wave solutions of explicit type, implicit type, and parametric type are obtained. These exact solutions include peculiar compacton solutions, singular periodic wave solutions, compacton‐like periodic wave solutions, periodic blowup solutions, smooth soliton solutions, and kink and antikink wave solutions. The great parts of them are different from the results in existing references. In order to show their dynamic profiles intuitively, the solutions of K(n, n), K(2n − 1, n), K(3n − 2, n), K(4n − 3, n), and K(m, 1) equations are chosen to illustrate with the concrete features.

Suggested Citation

  • Xianbin Wu & Weiguo Rui & Xiaochun Hong, 2012. "Exact Traveling Wave Solutions of Explicit Type, Implicit Type, and Parametric Type for K(m, n) Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:236875
    DOI: 10.1155/2012/236875
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    References listed on IDEAS

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    1. Ismail, M.S. & Taha, T.R., 1998. "A numerical study of compactons," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(6), pages 519-530.
    2. Xu, Chuanhai & Tian, Lixin, 2009. "The bifurcation and peakon for K(2,2) equation with osmosis dispersion," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 893-901.
    3. Zhu, Yonggui & Lü, Zhuosheng, 2006. "New exact solitary-wave special solutions for the nonlinear dispersive K(m,n) equations," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 836-842.
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    Cited by:

    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. Weiguo Rui & Yao Long, 2012. "Integral Bifurcation Method together with a Translation‐Dilation Transformation for Solving an Integrable 2‐Component Camassa‐Holm Shallow Water System," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Hasibun Naher & Farah Aini Abdullah, 2012. "The Improved (G’/G)‐Expansion Method for the (2+1)‐Dimensional Modified Zakharov‐Kuznetsov Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).

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