Periodic Peakon and Smooth Periodic Solutions for KP-MEW(3,2) Equation

In this paper, we consider the KP-MEW(3,2) equation by the bifurcation theory of dynamical systems when integral constant is considered. The corresponding traveling wave system is a singular planar dynamical system with one singular straight line. The phase portrait for , , and is drawn. Exact parametric representations of periodic peakon solutions and smooth periodic solution are presented.