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Solitary smooth hump solutions of the Camassa–Holm equation by means of the homotopy analysis method

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  • Abbasbandy, S.
  • Parkes, E.J.

Abstract

The homotopy analysis method is used to find a family of solitary smooth hump solutions of the Camassa–Holm equation. This approximate solution, which is obtained as a series of exponentials, agrees well with the known exact solution. This paper complements the work of Wu and Liao [Wu W, Liao S. Solving solitary waves with discontinuity by means of the homotopy analysis method. Chaos, Solitons & Fractals 2005;26:177–85] who used the homotopy analysis method to find a different family of solitary-wave solutions.

Suggested Citation

  • Abbasbandy, S. & Parkes, E.J., 2008. "Solitary smooth hump solutions of the Camassa–Holm equation by means of the homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 581-591.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:3:p:581-591
    DOI: 10.1016/j.chaos.2007.10.034
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    References listed on IDEAS

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    1. Shen, Jianwei & Xu, Wei & Li, Wei, 2006. "Bifurcations of travelling wave solutions in a new integrable equation with peakon and compactons," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 413-425.
    2. Wu, Wan & Liao, Shi-Jun, 2005. "Solving solitary waves with discontinuity by means of the homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 177-185.
    3. Tan, Yue & Xu, Hang & Liao, Shi-Jun, 2007. "Explicit series solution of travelling waves with a front of Fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 462-472.
    4. Parkes, E.J. & Vakhnenko, V.O., 2005. "Explicit solutions of the Camassa–Holm equation," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1309-1316.
    5. Kalisch, Henrik & Lenells, Jonatan, 2005. "Numerical study of traveling-wave solutions for the Camassa–Holm equation," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 287-298.
    6. Chen, Can & Tang, Minying, 2006. "A new type of bounded waves for Degasperis–Procesi equation," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 698-704.
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