On the solitary waves, breather waves and rogue waves to a generalized ([formula omitted])-dimensional Kadomtsev–Petviashvili equation

Abstract

Under investigation in this work is a generalized (3+1)-dimensional Kadomtsev–Petviashvili (GKP) equation, which can describe many nonlinear phenomena in fluid dynamics. By virtue of the Bell’s polynomials, an effective and straightforward way is presented to explicitly construct its bilinear form and soliton solution. Furthermore, based on the bilinear formalism and the extended homoclinic test method, the kinky breather wave solutions and rational breather wave solutions of the equation are well constructed. It is hoped that our results can be used to enrich the dynamical behavior of the (3+1)-dimensional nonlinear wave fields.