Differential and Integral Equations

Energy dependent scattering theory

David H. Sattinger and Jacek Szmigielski

Full-text: Open access

Abstract

We consider the scattering transform for Schrödinger operators with energy dependent potentials. We prove unique invertibility of the transform when there are no bound states and find a simplified recovery formula. We construct as a special case a one-soliton "breather". As an application we prove a global existence theorem for a class of non-linear partial differential equations.

Article information

Source
Differential Integral Equations, Volume 8, Number 5 (1995), 945-959.

Dates
First available in Project Euclid: 20 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1369056038

Mathematical Reviews number (MathSciNet)
MR1325540

Zentralblatt MATH identifier
0831.35152

Subjects
Primary: 34L25: Scattering theory, inverse scattering
Secondary: 34A55: Inverse problems 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 81U40: Inverse scattering problems

Citation

Sattinger, David H.; Szmigielski, Jacek. Energy dependent scattering theory. Differential Integral Equations 8 (1995), no. 5, 945--959. https://projecteuclid.org/euclid.die/1369056038


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