A new type of bounded waves for Degasperis–Procesi equation

In this paper we use integral method and numerical approach to show that Degasperis–Procesi equationut-uxxt+4uux=3uxuxx+uuxxx,ut-uxxt+4uux=3uxuxx+uuxxx,has new bounded waves which are defined on some semifinal bounded domains and possess properties of kink waves or antikink waves. Their implicit expressions are obtained. For a set of concrete data, the planar diagrams of the implicit expressions and their numerical simulations are displayed. It is seen that the planar diagrams are identical with the simulations.