  The inverse scattering transform for a special case of the 3-wave resonant
interaction equations with non-vanishing boundary conditions is studied. The
Jost solutions and the fundamental analytic solutions (FAS) for the associated
spectral problem are constructed. The inverse scattering problem for the Lax
operator is formulated as a Riemann-Hilbert problem on a Riemann surface. The
spectral properties of the Lax operator are formulated.
