Abstract
The travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation ut −uxxt + (1+b)umux = bux + uuxxx are considered where b > 1 and m are positive integers. The qualitative analysis methods of planar autonomous systems yield its phase portraits. Its soliton wave solutions, kink or antikink wave solutions, peakon wave solutions, compacton wave solutions, periodic wave solutions and periodic cusp wave solutions are obtained. Some numerical simulations of these solutions are also given.
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