Bifurcations of travelling wave solutions for a class of nonlinear fourth order variant of a generalized Camassa–Holm equation

In this paper, by using the bifurcation theory of dynamical systems for a class of nonlinear fourth order variant of a generalized Camassa–Holm equation, the existence of solitary wave solutions, breaking bounded wave solutions, compacton solutions and non-smooth periodic wave solutions are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of the above waves are determined.