Exact solutions to the integrable discrete nonlinear Schrodinger equation under a quasiscalarity condition

In this article we derive explicit solutions of the matrix integrable discrete nonlinear Schrodinger equation under a quasiscalarity condition by using the inverse scattering transform and the Marchenko method. The Marchenko equation is solved by separation of variables, where the Marchenko kernel is represented in the form $CA^{(n+j+1)} e^{i\tau(A-A^{-1}^2}B$, (A, B, C) being a matrix triplet where A has only eigenvalues of modulus larger than one. The class of solutions obtained contains the N-soliton and breather solutions as special cases. Unitarity properties of the scattering matrix are derived.