(1) South Ukrainian Pedagogical University, Odessa, Ukraine;(2) The Weizmann Institute of Science, Rehovot, Israel
Abstract:
The asymptotic scattering matrix sε(λ) for a Dirac-Krein system with signature matrix J = diag{ Ip,-Ip}, integrable potential, and the boundary condition u1(0, λ) = u2(0, λ)ε(λ) with a coefficient ε(λ) that belongs to the Schur class of holomorphic contractive p × p matrix-valued functions in the open upper half-plane is defined. The inverse asymptotic scattering problem for a given sε is analyzed by Krein’s method. Earlier studies by Krein and others focused on the case in which ε = Ip (or a constant unitary matrix).