A New Approach for Unique Restoration of a Time-Dependent Matrix Potential in a Hyperbolic Scattering Problem on the Semi-Axis

Abstract

This paper considers the inverse scattering problem on the semi-axis for the matrix hyperbolic system with a special structure of matrix potential. The possible relationship between the matrix scattering operators for the first order systems with unshifted and space-shifted potentials is given. By using this relationship, the new approach for unique restoration of this potential from the matrix scattering operators on the semi-axis is given.