Inverse Scattering on the Half-Line for a First-Order System with a General Boundary Condition

Abstract

The inverse scattering problem of recovering the matrix coefficient of a first-order system on the half-line from its scattering matrix is considered. In the case of a triangular structure of the matrix coefficient, this system has a Volterra-type integral transformation operator at infinity. Such a transformation operator allows to determine the scattering matrix on the half-line via the matrix Riemann–Hilbert factorization in the case, where the contour is real line, the normalization is canonical, and all the partial indices are zero. The ISP on the half-line is solved by reducing it to an ISP on the whole line for the considered system with the coefficients that are extended to the whole line by zero.