Inverse fixed angle scattering and backscattering for a  nonlinear Schrödinger equation in 2D

Georgios Fotopoulos; Markus Harju; Valery Serov

doi:10.3934/ipi.2013.7.183

Article Contents

2013, Volume 7, Issue 1: 183-197. Doi: 10.3934/ipi.2013.7.183

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Inverse fixed angle scattering and backscattering for a nonlinear Schrödinger equation in 2D

1.
Department of Mathematical Sciences, University of Oulu, PO Box 3000, FIN-90014 Oulu

Received: June 2012

Revised: November 2012

Published: February 2013

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Abstract

We investigate two inverse scattering problems for the nonlinear Schrödinger equation $$ -\Delta u(x) + h(x,|u(x)|)u(x) = k^{2}u(x), \quad x \in \mathbb{R}^2, $$ where $h$ is a very general and possibly singular combination of potentials. The method of Born approximation is applied for the recovery of local singularities and jumps from fixed angle scattering and backscattering data.

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Mathematics Subject Classification: 35P25, 35R30.

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