Inverse scattering problem for nonstrict hyperbolic system on the half-axis with a nonzero boundary condition

Abstract

Abstract The paper considers the scattering problem for the first-order system of hyperbolic equations on the half-axis with a nonhomogeneous boundary condition. This problem models the phnomennon of wave propagation in a nonstationary medium where an incoming wave unaffected by a potential field. The scattering operator on the half-axis with a nonzero boundary condition is defined and the uniqueness of the inverse scattering problem (the problem of finding the potential with respect to scattering operator) is studied.