Bifurcations and exact solutions of a new (3+1)-dimensional Kadomtsev-Petviashvili equation

Abstract

Based on the bifurcation theory, a new (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation is studied. The phase portraits of this equation are drawn, and some exact solutions, including solitons and periodic wave solutions, are derived. The (G′/G)-expansion method is applied to obtain many exact solutions, such as bright soliton, singular wave, and periodic wave solutions. Moreover, the interesting physical structures of these obtained solutions are described.