Lie symmetry analysis, Bäcklund transformations, and exact solutions of a (2 + 1)-dimensional Boiti-Leon-Pempinelli system

Abstract

In this paper, the Lie symmetry analysis method is employed to investigate the Lie point symmetries and the one-parameter transformation groups of a (2 + 1)-dimensional Boiti-Leon-Pempinelli system. By using Ibragimov’s method, the optimal system of one-dimensional subalgebras of this system is constructed. Truncated Painlevé analysis is used for deriving the Bäcklund transformation. The method of constructing lump-type solutions of integrable equations by means of Bäcklund transformation is first presented. Meanwhile, the lump-type solutions of the (2 + 1)-dimensional Boiti-Leon-Pempinelli system are obtained. The lump-type wave is one kind of rogue wave. The fusion-type N-solitary wave solutions are also constructed. In addition, this system is integrable in terms of the consistent Riccati expansion method.