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.
- Camassa–Holm equation
- homotopy analysis method
- series solution
Abbasbandy, S., & 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), 581-591. https://doi.org/10.1016/j.chaos.2007.10.034