Riemann-Hilbert Factorizations and Inverse Scattering for the AKNS-Equation with <i>L</i>¹-Potentials I

Abstract

A detailed group theoretic approach is developed for the 2 x 2 AKNS system with potentials supported on the half-line. This approach uses consistently Riemann-Hilbert splittings interpreted as factorizations in certain Banach Lie groups. In particular, it is shown how meromorphic splittings introduced by Beals and Coifman can be replaced with regular Riemann-Hilbert splittings leading to the group theoretic notion of a scattering data.