New exact periodic wave solutions for the Dullin–Gottwald–Holm equation

In this paper, the Dullin–Gottwald–Holm equation is studied using semi-inverse method and integral bifurcation method. New periodic waves such as peakon-like periodic wave, compacton-like periodic wave and singular periodic wave are found and their dynamical behaviors and certain strange phenomena are explained using the proposed criterion. The exact parametric representations of these waves are also presented.