Bifurcation of travelling wave solutions for the generalized Camassa–Holm–KP equations

By using the bifurcation theory of planar dynamical systems to the generalized Camassa–Holm–KP equations, the existence of smooth and non-smooth travelling wave solutions is proved. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of above solutions are given. Some exact explicit parametric representations of the above waves are determined.