Bäcklund transformations, symmetry reductions and exact solutions of (2+1)-dimensional nonlocal DS equations

Abstract

In this paper, the CK direct method is applied to the nonlocal equations for the first time, the new Bäcklund transformations, non-Lie group transformations and exact solutions of the (2+1)-dimensional nonlocal DS equation are obtained. In particular, the expression of infinite exact solutions of nonlocal DS equation is given. In order to establish the relation with Lie group, the Bäcklund transformation of nonlocal DS equation is transformed into Lie transformation by variable transformation, and then the (2+1)-dimensional nonlocal equation is reduced into (1+1)-dimensional nonlocal equation. We also give the Lax pair of the reduced nonlocal equation and prove that the equation is integrable. The content of this paper enriches the research on the theory of nonlocal equations and is helpful for the construction of exact solutions of other nonlocal equations.