Multicomponent NLS-Type Equations on Symmetric Spaces and Their Reductions

We analyze the fundamental properties of models of the multicomponent nonlinear Schrodinger (NLS) type related to symmetric spaces and construct new types of reductions of these systems. We briefly describe the spectral properties of the Lax operators L, which in turn determine the corresponding recursion operator Л and the fundamental properties of the relevant class of nonlinear evolution equations. The results are illustrated by specific examples of NLS-type systems related to the $\bold{DIII}$ symmetric space for the $so(8)$ algebra.