Abstract
In this paper, we construct two families of new explicit exact traveling wave solutions of the Camassa–Holm equation which solve an open problem in the previous paper [Zhang G, Qiao ZJ, Liu F. Cuspons and smooth solitons of the Camassa-Holm equation under an inhomogeneous boundary condition. Pac J Appl Math. 2007;1(1):113–130]. With the help of the numerical graphs and a profound mathematical analysis, we discovered the analytic formulas for those two explicit exact solutions.
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