Inverse scattering problem for linear system of four-wave interaction problem with equal number of incident and scattered waves

Abstract

The first order semi-strict hyperbolic system on the semi-axis in the case of equal number of incident and scattered waves are considered. The uniqueness of the inverse scattering problem (the problem of finding the potential with respect to scattering operator) is studied by utilizing it to Gelfand–Levitan–Marchenko type linear integral equations. It is determined the sufficient quantity of scattering problems (on the semi-axis for the same hyperbolic system) for ensuring the uniqueness of the inverse scattering problem.