CLOSED FORM SOLUTIONS TO THE INTEGRABLE DISCRETE NONLINEAR SCHRÖDINGER EQUATION

摘要

In this article we derive explicit solutions of the matrix integrable discrete nonlinear Schr¨odingerudequation by using the inverse scattering transform and the Marchenko method. The Marchenkoudequation is solved by separation of variables, where the Marchenko kernel is represented in separatedudform, using a matrix triplet (A,B,C). Here A has only eigenvalues of modulus larger than one. Theudclass of solutions obtained contains the N-soliton and breather solutions as special cases. We alsoudprove that these solutions reduce to known continuous matrix NLS solutions as the discretizationudstep vanishes.