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.