Some discrete solitons and interaction dynamical behaviors for a PT-symmetric discrete nonlocal nonlinear Schrödinger equation

Abstract

At present, there have been many achievements on the study of integrable nonlocal nonlinear Schrödinger (NNLS) equation, which can enrich the mathematical structure of the NNLS equation by adding the discrete conditions. Ablowitz proposed a method to solve the nonlocal discrete Schrödinger equation under decaying boundary conditions by using the inverse scattering transformation. At this stage, there are few work of the discrete nonlocal nonlinear Schrödinger(DNNLS) equation with PT-symmetric. A detailed study of the DNNLS equation with PT-symmetric under fast decaying boundary conditions is carried out by using Darboux transformation method, which obtains the novel formulation of the soliton solution with the 2 × 2 Lax pairs, then some dynamical behaviors of the novel soliton solutions are analyzed by selecting different seed solutions and the wave parameters.