Inverse Scattering Problem for LinearSystem of Four-Wave Interaction Problemon the Half-Line with a General BoundaryCondition

Abstract

The first order hyperbolic system of four equations on the semi-axis in thecase of equal numbers of incident and scattered waves are considered whenthe velocities of the scattering waves are coincident. It is determined thecriteria for inverse scattering problem (the problem of finding the potentialwith respect to scattering operator) in terms of transmission matrices intwo different boundary conditions. The uniqueness of the inverse scatteringproblem is studied by utilizing it to Gelfand–Levitan–Marchenko type linearintegral equation.