A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy

Evgeny L. Lakshtanov; Roman G. Novikov; Boris R. Vainberg

doi:10.13137/2464-8728/13150

A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy

Evgeny L. Lakshtanov, Roman G. Novikov, Boris R. Vainberg

Research output: Contribution to journal › Article › peer-review

Abstract

We develop the Riemann-Hilbert problem approach to inverse scattering for the two-dimensional Schoodinger equation at fixed energy. We obtain global or generic versions of the key results of this approach for the case of positive energy and compactly supported potentials. In particular, we do not assume that the potential is small or that Faddeev scattering solutions do not have singularities (i.e. we allow the Faddeev exceptional points to exist). Applications of these results to the Novikov-Veselov equation are also considered.

Original language	English
Pages (from-to)	21-47
Number of pages	27
Journal	Rendiconti dell'Istituto di Matematica dell'Universita di Trieste
Volume	48
Issue number	1
DOIs	https://doi.org/10.13137/2464-8728/13150
Publication status	Published - 1 Jan 2016

Keywords

Faddeev functions
Generalized Riemann-Hilbert-Manakov problem
Novikov-Veselov equation
Two-dimensional inverse scattering

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10.13137/2464-8728/13150

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abstract = "We develop the Riemann-Hilbert problem approach to inverse scattering for the two-dimensional Schoodinger equation at fixed energy. We obtain global or generic versions of the key results of this approach for the case of positive energy and compactly supported potentials. In particular, we do not assume that the potential is small or that Faddeev scattering solutions do not have singularities (i.e. we allow the Faddeev exceptional points to exist). Applications of these results to the Novikov-Veselov equation are also considered.",

keywords = "Faddeev functions, Generalized Riemann-Hilbert-Manakov problem, Novikov-Veselov equation, Two-dimensional inverse scattering",

author = "Lakshtanov, \{Evgeny L.\} and Novikov, \{Roman G.\} and Vainberg, \{Boris R.\}",

year = "2016",

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AU - Lakshtanov, Evgeny L.

AU - Novikov, Roman G.

AU - Vainberg, Boris R.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - We develop the Riemann-Hilbert problem approach to inverse scattering for the two-dimensional Schoodinger equation at fixed energy. We obtain global or generic versions of the key results of this approach for the case of positive energy and compactly supported potentials. In particular, we do not assume that the potential is small or that Faddeev scattering solutions do not have singularities (i.e. we allow the Faddeev exceptional points to exist). Applications of these results to the Novikov-Veselov equation are also considered.

AB - We develop the Riemann-Hilbert problem approach to inverse scattering for the two-dimensional Schoodinger equation at fixed energy. We obtain global or generic versions of the key results of this approach for the case of positive energy and compactly supported potentials. In particular, we do not assume that the potential is small or that Faddeev scattering solutions do not have singularities (i.e. we allow the Faddeev exceptional points to exist). Applications of these results to the Novikov-Veselov equation are also considered.

KW - Faddeev functions

KW - Generalized Riemann-Hilbert-Manakov problem

KW - Novikov-Veselov equation

KW - Two-dimensional inverse scattering

U2 - 10.13137/2464-8728/13150

DO - 10.13137/2464-8728/13150

M3 - Article

AN - SCOPUS:85009914366

SN - 0049-4704

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SP - 21

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JO - Rendiconti dell'Istituto di Matematica dell'Universita di Trieste

JF - Rendiconti dell'Istituto di Matematica dell'Universita di Trieste

IS - 1

ER -

A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy

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Keywords

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