Application of the integral bifurcation method for solving modified Camassa–Holm and Degasperis–Procesi equations Original Research Article

By using the integral bifurcation method, the modified form of Camassa–Holm and Degasperis–Procesi equations are studied. Under the two different transformations, we obtain many new travelling wave solutions including loop soliton solutions, peakon solutions, solitary wave solutions and periodic wave solutions in addition to bell-shaped solitary wave solutions and peakon solutions offered by Liu and Ouyang. In particular, under the same parametric conditions, two kinds of different bifurcations of travelling wave solution are found.