Inverse scattering on the half-line for generalized ZS-AKNS system with general boundary conditions

Abstract

The inverse scattering problem for a first order system of three equations on the half-line with nonsingular diagonal matrix multiplying the derivative and general boundary conditions is considered. It is focused the case of two repeated diagonal elements of diagonal matrix. The scattering matrix on the half line is defined and a unique restoration of the potential from the scattering matrix is proved. The possible application to integration of integro-differential four-wave interaction problem is also focused.