Differential and Integral Equations

Energy dependent inverse scattering on the line

Yutaka Kamimura

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Abstract

We give a complete solution to the inverse scattering problem for the energy dependent Schrödinger equation on the full line when there are no bound states. This solution characterizes the image of the energy dependent scattering transform, generalizes the Deift-Trubowitz theorem for the standard Schrödinger equation in the absence of bound states, and indicates clearly the inverse transform by a simple inversion formula.

Article information

Source
Differential Integral Equations, Volume 21, Number 11-12 (2008), 1083-1112.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1355502295

Mathematical Reviews number (MathSciNet)
MR2482498

Zentralblatt MATH identifier
1224.81017

Subjects
Primary: 81U40: Inverse scattering problems
Secondary: 34A55: Inverse problems 34L25: Scattering theory, inverse scattering

Citation

Kamimura, Yutaka. Energy dependent inverse scattering on the line. Differential Integral Equations 21 (2008), no. 11-12, 1083--1112. https://projecteuclid.org/euclid.die/1355502295


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