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

Abstract

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 n(1) (1 <= n(1) <= n-1) incident and n(2) (n(2) = n-n(2)) scattered waves. In case n(1) is divisible by n(2), we formulate the inverse scattering problem for a nonstationary Dirac-type system when considering m (m = n(1)/n(2)) 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. (c) 2008 Elsevier Inc. All rights reserved.