New exact traveling wave solutions for the modified form of Degasperis–Procesi equation

With the aid of symbolic computation, a generalized auxiliary equation method is proposed to construct more general exact solutions to some types of NLPDEs. In this letter, using the auxiliary equation method, some new solitary and traveling wave solutions of such nonlinear mDP equations given by ut-uxxt+4u2ux=3uxuxx+uuxxxut-uxxt+4u2ux=3uxuxx+uuxxx are obtained in a very general form. Several interesting special cases of these general solutions are also discussed.