Discrete soliton solutions for a generalized discrete nonlinear Schrödinger equation with variable coefficients via discrete N-fold Darboux transformation

Under investigations in this paper is a discrete generalized nonlinear Schrödinger equation with variable coefficients. Through symbolic computation the discrete spectral problems are analyzed, the discrete N-fold Darboux transformation (DT) is constructed, discrete one and two-soliton solutions in the form of Vandermonde-like determinants are derived and some dynamic behaviors of those solitons are discussed graphically.