Bifurcations and exact traveling wave solutions for a modified Degasperis–Procesi equation

In this paper, the bifurcations of a modified Degasperis–Procesi equation are studied under different parametric conditions, which have not been investigated by the bifurcation theory of dynamical systems before. The existence of loop, periodic wave and smooth solitary wave solutions for the modified Degasperis–Procesi equation is proved, and exact expressions of corresponding traveling wave solutions are obtained.