Quasi-Periodic Solutions for matrix nonlinear Schroedinger Equations

The Adler-Kostant-Symes theorem yields isospectral hamiltonian flows on the dual $\tilde\grg^{+*}$ of a Lie subalgebra $\tilde\grg^+$ of a loop algebra $\tilde\grg$. A general approach relating the method of integration of Krichever, Novikov and Dubrovin to such flows is used to obtain finite-gap solutions of matrix Nonlinear Schr\"odinger Equations in terms of quotients of $\tet$-functions.