Novel formulation of inverse scattering and characterization of scattering data

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2011, 2011(Special): 343-350. doi: 10.3934/proc.2011.2011.343

Novel formulation of inverse scattering and characterization of scattering data

Francesco Demontis ^1, and Cornelis Van der Mee ^1,

1.	Dip. Matematica e Informatica, Università di Cagliari, Viale Merello 92, 09121 Cagliari, Italy, Italy

Received July 2010 Revised January 2011 Published October 2011

Abstract
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In this article we formulate the direct and inverse scattering theory for the focusing matrix Zakharov-Shabat system as the construction of a 1, 1-correspondence between focusing potentials with entries in $L^1(\mathbb{R})$ and Marchenko integral kernels, given the fact that these kernels encode the usual scattering data (one reflection coecient, the discrete eigenvalues with positive imaginary part, and the corresponding norming constants) faithfully. In the re ectionless case, we solve the Marchenko equations explicitly using matrix triplets and obtain focusing matrix NLS solutions in closed form.

Keywords: Characterization of Scattering Data, Inverse Scattering Transform, Marchenko equation.

Mathematics Subject Classification: Primary: 35Q55, 37K15.

Citation: Francesco Demontis, Cornelis Van der Mee. Novel formulation of inverse scattering and characterization of scattering data. Conference Publications, 2011, 2011 (Special) : 343-350. doi: 10.3934/proc.2011.2011.343

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