Differential and Integral Equations

Energy dependent inverse scattering on the line

Yutaka Kamimura

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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

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

First available in Project Euclid: 14 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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