Abundant invariant solutions of extended (3+1)-dimensional KP–Boussinesq equation

Abstract Lie group analysis method is applied to the extended (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation and the corresponding similarity reduction equations are obtained with various infinitesimal generators. By selecting suitable arbitrary functions in the similarity reduction solutions, we obtain abundant invariant solutions, including the trigonometric solution, the kink-lump interaction solution, the interaction solution between lump wave and triangular periodic wave, the two-kink solution, the lump solution, the interaction between a lump and two-kink and the periodic lump solution in different planes. These exact solutions are also given graphically to show the detailed structures of this high dimensional integrable system.