New ansätz for obtaining wave solutions of the generalized Camassa–Holm equation

An alternate approach is proposed for obtaining periodic wave and peaked solitary wave solutions of the following nonlinear generalized Camassa–Holm equationut+2kux-uxxt+aumux=2uxuxx+uuxxxFor m = 1, 2, 3 we give the explicit expressions for the peakons. The ansätz, introduced in this paper, will also demonstrate the existence of a new class of discontinuous soliton solutions with infinite spikes.