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Solitary smooth hump solutions of the Camassa-Holm equation by means of the homotopy analysis method. (English) Zbl 1139.76013
Summary: We use the homotopy analysis method to find a family of solitary smooth hump solutions of Camassa-Holm equation. This approximate solution, which is obtained as a series in exponentials, agrees well with the known exact solution. This paper complements the work of W. Wu and S. Liao [ibid. 26, No. 1, 177–185 (2005; Zbl 1071.76009)] who used the homotopy analysis method to find a different family of solitary-wave solutions.

MSC:
76B25 Solitary waves for incompressible inviscid fluids
76M25 Other numerical methods (fluid mechanics) (MSC2010)
35Q51 Soliton equations
Keywords:
series solution
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