Explicit and implicit solutions of a generalized Camassa–Holm Kadomtsev–Petviashvili equation

In this paper, a generalized Camassa–Holm Kadomtsev–Petviashvili (gCH–KP) equation is studied. As a result, under different parameter conditions, the bounded travelling wave solutions such as periodic waves, periodic cusp waves, solitary waves, peakons, loops and kink waves are given, and the dynamic characters of these solutions are investigated.

► Nonlinear CH–KP equations have practical applications in science.
► The CH–KP equations have rich structures of the bounded travelling.
► The exact solutions and simulations of the bounded travelling are important to know dynamic characters of CH–KP.