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

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.