CLOSED FORM SOLUTIONS TO THE INTEGRABLE DISCRETE NONLINEAR SCHRÖDINGER EQUATION

In this article we derive explicit solutions of the matrix integrable discrete nonlinear Schr¨odinger equation 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 separated form, using a matrix triplet (A,B,C). Here A has only eigenvalues of modulus larger than one. The class of solutions obtained contains the N-soliton and breather solutions as special cases. We also prove that these solutions reduce to known continuous matrix NLS solutions as the discretization step vanishes.