New explicit periodic wave solutions and their limits for modified form of Camassa-holm equation

Abstract

In this paper, we consider the following nonlinear equationwhich is a modified form of the Camassa-Holm equation. We construct four new explicit periodic wave solutions by bifurcation method of dynamical systems. We also obtain two explicit solitary wave solutions via the limits of the explicit periodic wave solutions. One of the two solitary wave solutions is new.