A discretization of the matrix nonlinear Schroedinger equation

In this paper, we shall show that a class of solutions to the discrete coupled matrix nonlinear Schroedinger equation (DCMNLSE) is gauge equivalent to the discrete equation of the Schroedinger flow of maps into the Grassmannian and the realizing gauge transformation is only the discretization of a classical gauge transformation between the matrix nonlinear Schroedinger equation (MNLSE) and the Schrödinger flow of maps into the Grassmannian. In other words, from the viewpoint of gauge equivalence, a class of solutions of the DCMNLSE is a correct discretization of the MNLSE. (author)