Group invariant solutions of (3+1)-dimensional generalized B-type Kadomstsev Petviashvili equation using optimal system of Lie subalgebra

Abstract In fluid mechanics and ocean engineering, the (3+1)-dimensional B-type KP equations have attracted a good size of recent research. In this paper, the Lie group analysis is used to carry out the similarity reduction and exact solutions of the (3+1)-dimensional generalized B-type KP type equation. We constructed infinitesimal generators, commutation relations, adjoint table and symmetry groups for this equation. Also, the one dimensional optimal system of subalgebra is presented with adjoint representation. Based on the optimal system, similarity reductions to partial differential equations (PDEs) are obtained. Moreover, PDEs are reduced to ordinary differential equations by one-dimensional optimal system of subalgebras, and the similarity solutions are provided, including periodic solutions, travelling wave solutions, elliptic function solutions and solutions in terms of hyper-geometric function and Airy type functions.