On the 3-wave Equations with Constant Boundary Conditions
  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. 
Vladimir S. Gerdjikov and Georgi G. Grahovski
nlin.SI math-ph math.MP