Inverse scattering problem for the non-stationary matrix Dirac equation on the half-plane with the singular transmission matrix in the boundary condition

Abstract

The inverse scattering problem for a non-stationary matrix Dirac equation on the half-plane with the boundary condition which includes a singular transmission matrix is considered. A class of potential related to the rank of the transmission matrix is determined for which such a potential is uniquely reconstructed from the scattering operator. The description of the scattering operator, which is an important problem in the theory of inverse scattering problems, is considered in the paper.