Abundant invariant solutions of (3+1)-dimensional combined pKP-BKP equation

Abstract Lie symmetry analysis is applied to a (3+1)-dimensional combined potential Kadomtsev–Petviashvili equation with B-type Kadomtsev–Petviashvili equation (pKP-BKP equation) and the corresponding similarity reduction equations are obtained with the different infinitesimal generators. Invariant solutions with arbitrary functions and constants for the (3+1)-dimensional pKP-BKP equation, including the lump solution, the periodic-lump solution, the two-kink solution, the breather solution and the lump–two-kink solution, have been studied analytically and graphically.