Compacton-like wave and kink-like wave of GCH equation

In this paper, we combine qualitative analysis with numerical exploration to study traveling waves of a generalized Camassa–Holm equation. Two new types of bounded traveling waves are found. One of them is called compacton-like wave because it is of some properties of compacton. Similarly, the other is called kink-like wave since it possesses some properties of kink. Their implicit expressions are obtained. For some concrete data, the diagrams of the implicit functions are displayed, and the numerical simulation is made. The results imply that our theoretical analysis is agreeable with the numerical simulation.