JournalsprimsVol. 29 , No. 6DOI 10.2977/prims/1195166423

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

  • Josef Dorfmeister

    TU München, Germany
  • Jacek Szmigielski

    University of Kansas, Lawrence, USA
Riemann-Hilbert Factorizations and Inverse Scattering for the AKNS-Equation with <i>L</i><sup>1</sup>-Potentials I cover

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.