A discretization of the matrix nonlinear Schrodinger equation

In this paper, we shall show that a class of solutions to the discrete coup led matrix nonlinear Schrodinger equation (DCMNLSE) is gauge equivalent to the discrete equation of the Schrodinger flow of maps into the Grassmannian and the realizing gauge transformation is only the discretization of a cla ssical gauge transformation between the matrix nonlinear Schrodinger equati on (MNLSE) and the Schrodinger flow of maps into the Grassmannian. In other words, from the viewpoint of gauge equivalence, a class of solutions of th e DCMNLSE is a correct discretization of the MNLSE.