Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry]
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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2010, Volume 6, Number 1, Pages 21–33 (Mi jmag139)  
This article is cited in 9 scientific papers (total in 9 papers)

A Paley–Wiener theorem for periodic scattering with applications to the Korteweg–de Vries equation

I. Egorovaa, G. Teschlbc

a Mathematical Division, B. Verkin Institute for Low Temperature Physics and Engineering, 47 Lenin Ave., Kharkiv, 61103, Ukraine
b International Erwin Schrödinger Institute for Mathematical Physics, 9 Boltzmanngasse, 1090, Wien, Austria
c University of Vienna
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Abstract: A one-dimensional Schrödinger operator which is a short-range perturbation of a finite-gap operator is considered. There are given the necessary and sufficient conditions on the left/right reflection coefficient such that the difference of the potentials has finite support to the left/right, respectively. Moreover, these results are applied to show a unique continuation type result for solutions of the Korteweg–de Vries equation in this context. By virtue of the Miura transform an analogous result for the modified Korteweg–de Vries equation is also obtained.
Key words and phrases: inverse scattering, finite-gap background, KdV, nonlinear Paley–Wiener Theorem.
Received: 02.11.2009
Bibliographic databases:
Document Type: Article
MSC: Primary 34L25, 35Q53; Secondary 35B60, 37K20
Language: English
Citation: I. Egorova, G. Teschl, “A Paley–Wiener theorem for periodic scattering with applications to the Korteweg–de Vries equation”, Zh. Mat. Fiz. Anal. Geom., 6:1 (2010), 21–33
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
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