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

Abbasbandy, S. and Parkes, E.J. (2008) Solitary smooth hump solutions of the Camassa-Holm equation by means of the homotopy analysis method. Chaos, Solitons and Fractals, 36 (3). pp. 581-591. ISSN 0960-0779

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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 & 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.