## Differential and Integral Equations

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

### Energy dependent inverse scattering on the line

#### 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