On the N-waves hierarchy with constant boundary conditions. Spectral properties.

This paper is devoted to N -wave equations with constant boundary conditions related to symplectic Lie algebras. We study the spectral properties of a class of Lax operators L , whose potentials Q (x , t) tend to constants Q ± for x → ± ∞. For special choices of Q ± , we outline the spectral properties of L , the direct scattering transform and construct its fundamental analytic solutions. We generalize Wronskian relations for the case of CBC — this allows us to analyze the mapping between the scattering data and the x -derivative of the potential Q x . Next, using the Wronskian relations, we derive the dispersion laws for the N -wave hierarchy and describe the NLEE related to the given Lax operator. [ABSTRACT FROM AUTHOR]