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2015, 2015(special): 1089-1097. doi: 10.3934/proc.2015.1089

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

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

Received  September 2014 Revised  February 2015 Published  November 2015

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.
Citation: Cornelis van der Mee. Direct scattering of AKNS systems with $L^2$ potentials. Conference Publications, 2015, 2015 (special) : 1089-1097. doi: 10.3934/proc.2015.1089
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##### References:
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