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Decomposition method for the Camassa–Holm equation

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  • J. Sadefo Kamdem

    (Equations aux Dérivées Partielles et Physique Mathématique - - URCA - Université de Reims Champagne-Ardenne)

  • Zhijun Qiao

    (UTPA - University of Texas-Pan American - University of Texas-Pan)

Abstract

The Adomian decomposition method is applied to the Camassa–Holm equation. Approximate solutions are obtained for three smooth initial values. These solutions are weak solutions with some peaks. We plot those approximate solutions and find that they are very similar to the peaked soliton solutions. Also, one single and two anti-peakon approximate solutions are presented. Compared with the existing method, our procedure just works with the polynomial and algebraic computations for the CH equation.

Suggested Citation

  • J. Sadefo Kamdem & Zhijun Qiao, 2007. "Decomposition method for the Camassa–Holm equation," Post-Print hal-02938583, HAL.
    • Handle: RePEc:hal:journl:hal-02938583
    DOI: 10.1016/j.chaos.2005.09.071
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    References listed on IDEAS

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    1. Ragnisco, O. & Bruschi, M., 1996. "Peakons, r-matrix and Toda lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 228(1), pages 150-159.
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    Cited by:

    1. Elgazery, Nasser S., 2008. "Numerical solution for the Falkner–Skan equation," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 738-746.
    2. Ramos, J.I., 2009. "Piecewise-adaptive decomposition methods," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1623-1636.
    3. Abdel-Halim Hassan, I.H., 2008. "Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 53-65.
    4. Jules Sadefo-Kamdem, 2011. "Integral Transforms With The Homotopy Perturbation Method And Some Applications," Working Papers hal-00580023, HAL.
    5. Lv, Na & Mei, Jian-Qin & Zhang, Hong-Qing, 2012. "Differential form method for finding symmetries of a (2+1)-dimensional Camassa–Holm system based on its Lax pair," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 503-506.

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