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

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. • A new (3+1)-dimensional Kadomtsev-Petviashvili equation is investigated. • The phase portraits of this equation by bifurcation theory are drawn. • The model is solved using the (G'/G)-expansion method. • Some soliton, singular and periodic wave solutions are derived. [ABSTRACT FROM AUTHOR]