Characteristics of the solitary waves and rogue waves with interaction phenomena in a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation

Abstract

Under investigation in this work is a generalized ( 3 + 1 )-dimensional Kadomtsev–Petviashvili equation, which can describe many nonlinear phenomena in fluid dynamics. By virtue of Bell’s polynomials, an effective and straightforward way is presented to explicitly construct its bilinear form and soliton solutions. Furthermore, based on the bilinear formalism, a direct method is employed to explicitly construct its rogue wave solutions with an ansätz function. Finally, the interaction phenomena between rogue waves and solitary waves are presented with a detailed derivation. The results can be used to enrich the dynamical behavior of higher dimensional nonlinear wave fields.