Direct scattering of AKNS systems  with $L^2$ potentials

Cornelis van der  Mee

doi:10.3934/proc.2015.1089

Article Contents

2015, Volume 2015: 1089-1097. Doi: 10.3934/proc.2015.1089 open access

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Direct scattering of AKNS systems with $L^2$ potentials

Cornelis van der Mee^1,

1.
Dip. Matematica e Informatica, Università di Cagliari, Viale Merello 92, 09123 Cagliari

Received: September 2014

Revised: February 2015

Published: October 2015

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Abstract

In this article the Jost solutions of the AKNS system with suitably weighted $L^2$ potential are constructed as Hardy space perturbations of their space-infinity asymptotics. The reflection coefficients are proven to be $L^2$-functions when the transmission coefficients are $L^\infty$-functions.

Keywords:

AKNS system,
characterization of scattering data.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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