New Peakons and Periodic Peakons of the Modified Camassa-Holm Equation

Abstract

In this paper, we obtain new peakon and periodic peakon solutions to a modified Camassa-Holm equation. We change the modified Camassa-Holm equation into a planar system. Then the first integral and algebraic curves of this system are obtained. By using the first integral and algebraic curves, a new peakon solution is given by hyperbolic function. Moreover, some new periodic peakons are given by elliptic functions and triangle functions.