Inverse scattering transform for the higher-order integrable discrete nonlinear Schrödinger equation with nonzero boundary conditions

The inverse scattering transform is a tool for solving the initial value problem of nonlinear equations, and the solution of the initial-value problem by inverse scattering transform proceeds in three steps: direct scattering, time evolution and inverse problem. In this paper, we discuss the higher-order integrable discrete nonlinear Schr & ouml;dinger equation which is subjected to inverse scattering transform under nonzero boundary conditions, and the corresponding soliton solutions are obtained and illustrated.