Exact Peakon, Periodic Peakon and Solitary Wave Solutions of Generalized Camassa–Holm Equations

This paper is concerned with the traveling wave solutions of the generalized Camassa–Holm equations. By converting the associated traveling wave system to a singular system of the first class, we investigate the bifurcations of traveling wave solutions via the planar dynamical system theory under varying parameters. In addition, exact explicit expressions are derived for solitary wave solutions, peakon solutions, pseudo-peakon solutions, and periodic peakon solutions.