Bäcklund transformations, nonlocal symmetry and exact solutions of a generalized (2+1)-dimensional Korteweg–de Vries equation

Abstract

In this paper, nonlocal residual symmetry of a generalized (2+1)-dimensional Korteweg–de Vries equation is derived with the aid of truncated Painlevé expansion. Three kinds of non-auto and auto Bäcklund transformations are established. The nonlocal symmetry is localized to a Lie point symmetry of a prolonged system by introducing auxiliary dependent variables. The linear superposed multiple residual symmetries are presented, which give rise to the nth Bäcklund transformation. The consistent Riccati expansion method is employed to derive a Bäcklund transformation. Furthermore, the soliton solutions, fusion-type N-solitary wave solutions and soliton–cnoidal wave solutions are gained through Bäcklund transformations.