  The 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 $Q_\pm$ for
$x\to \pm \infty$. For special choices of $Q_\pm$ we outline the spectral
properties of $L$, the direct scattering transform and construct its
fundamental analytic solutions. We generalise Wronskian relations for the case
of CBC -- this allows us to analyse 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.
