Darboux coordinates and quasiperiodic solutions for matrix nonlinear shrodinger equations

Following a general method, the phase space underlying finte gap solutions for matrix nonlinear Schrodinger equations is parametrized by Darboux coordinates from a finite dimensional vector space via moment map. The matrix NLS equations are recovered as commutativity conditions of Lax equations on a loop algebra which are given in Hamiltonian form by the Adler-Kostant-Symes (AKS) theorem. Quasiperiodic solutions in terms of quotients of circle-minus-functions are computed with the Krichever-Novikov-Dubrovin (KN,D) integration method. (Author) 9 refs