Factorization technique and new exact solutions for the modified Camassa–Holm and Degasperis–Procesi equations

In this paper, the recent factorization technique is applied to the modified Camassa–Holm and Degasperis–Procesi equations and two first-order ordinary differential equations are obtained, respectively. Subsequently, some new exact solitary wave solutions for the two equations are proposed. The figures for the bell-type and peakon-type solutions of the modified Camassa–Holm are plotted to describe the properties of the solutions.