Inverse scattering problem for nonstationary Dirac-type systems on the half-plane

In this paper was considered the scattering problem for the nonstationary Dirac-type systems of n (n⩾2) equations on the half-plane when the system has n1 (1⩽n1⩽n−1) incident and n2 (n2=n−n1) scattered waves. In case n1 is divisible by n2, we formulate the inverse scattering problem for a nonstationary Dirac-type system when considering m () scattering problems on the half-plane with the same incident waves but different boundary conditions. Moreover, the scattering operator for the nonstationary Dirac-type system on half-plane was defined and unique restoration of the potential with respect to the scattering operator was proved.