Exact solutions for the Davey-Stewartson I equation obtained from auto-Bäcklund transformation related to nonlocal residual symmetry

Abstract

In this paper, the nonlocal residual symmetry associated with the Painlevé truncation expansion of the Davey-Stewartson I equation is derived. After localizing the nonlocal symmetry into a local one and solving the corresponding initial value problem, the auto-Bäcklund transformation related to this nonlocal symmetry is presented. Making full use of the auto-Bäcklund transformation, different types of exact solutions for the Davey-Stewartson I equation can be constructed. Here, by selecting the seed expansion function as an exponential function, a rational function, etc., the soliton solution, solitoff solution, rogue wave solution and soliton-periodic wave interaction solution to the Davey-Stewartson I equation are designed. To specifically analyze their dynamic behaviors, the three-dimensional evolution profiles and density plots for these exact solutions with particular choices of the involved free parameters are effectively illustrated.