  Two discretizations of the vector nonlinear Schrodinger (NLS) equation are
studied. One of these discretizations, referred to as the symmetric system, is
a natural vector extension of the scalar integrable discrete NLS equation. The
other discretization, referred to as the asymmetric system, has an associated
linear scattering pair. General formulae for soliton solutions of the
asymmetric system are presented. Formulae for a constrained class of solutions
of the symmetric system may be obtained. Numerical studies support the
hypothesis that the symmetric system has general soliton solutions.
