Some general bright soliton solutions and interactions for a (2＋1)-dimensional nonlocal nonlinear Schrödinger equation

Abstract

In this paper, a novel application of Darboux transformation is presented for (2＋1)-dimensional nonlocal nonlinear Schrödinger equation. The Darboux transformation is a power method to solve some (1＋1)-dimensional classical nonlinear Schrödinger (NLS) equations, however, there is less work of (2＋1)-dimensional ((2＋1)-D) nonlocal nonlinear Schrödinger(NNLS) equation with Darboux transformation. With the development of science, the NNLS equation gradually appears, where the nonlocality is the reverse spatial field or reverse time field. We focus on how to solve the (2＋1)-D NNLS equation with reverse time field q(x,y,−t). Using the Darboux transformation, some novel (2＋1)-D nonlocal soliton solutions are derived on a background of kink waves, including 1-soliton solution, 2-soliton solution, bright soliton and soliton interaction on kink wave backgrounds. This method is a novel application of Darboux transformation, which can be extend to some other nonlocal nonlinear or higher-dimensional soliton equations on kink wave backgrounds.