Logarithm transformation together with the integral bifurcation method for investigating exact solutions of the CDF equation with mKdV type

Abstract

In this paper, under a logarithm transformation, by using the integral bifurcation method, we study the Cologero–Degasperis–Fokas equation with mKdV type, which was introduced by Cologero, Degasperis and Fokas. Some exact traveling wave solutions such as smooth solitary wave solutions, smooth periodic wave solutions, kink wave solutions, singular kink wave solution, singular periodic wave solutions, blowup soliton solution and singular blowup wave solution are obtained. We show their profiles and discuss their dynamic properties aim at some typical solutions.