Existence of the Periodic Peaked Solitary-Wave Solutions to the Camassa–Holm–Kadomtsev–Petviashvili Equation

Abstract

Considered in this paper is the Camassa–Holm–Kadomtsev–Petviashvili (CH–KP) equation [22], which can be obtained as a model for the propagation of shallow water waves over a flat bed. It is shown that the existence of periodic peaked solitary-wave solutions to this model equation. In addition, we show that there are a multitude of solitary waves such as smooth, peakons, cuspons, stumpons, and composite like as CH equation.