Multicomponent nonlinear schrödinger equations with constant boundary conditions

We outline several specific issues concerning the theory of multicomponent nonlinear Schrödinger equations with constant boundary conditions. We first study the spectral properties of the Lax operator $L$, the structure of the phase space $\mathcal M$, and the construction of the fundamental analytic solutions. We then consider the regularized Wronskian relations, which allow analyzing the map between the potential of $L$ and the scattering data. The Hamiltonian formulation also requires a regularization procedure.