Stability analysis, soliton waves, rogue waves and interaction phenomena for the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation

Abstract

In this paper, the (3[Formula: see text]+[Formula: see text]1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation is discussed, which can be used to describe certain characteristics of soliton in a nonlinear media with weak dispersion. By using the virtue of Bell polynomial, we construct the exact bilinear formalism and soliton wave of the equation, respectively. We also analyze its stability analysis. Moreover, based on the resulting bilinear formalism, we obtain its rouge wave solutions with a direct method. Finally, we also discuss the interaction phenomena between solitary wave solutions and rogue wave solutions. It is hoped that our results can be used to enrich the dynamics of the (3[Formula: see text]+[Formula: see text]1)-dimensional nonlinear wave fields.