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

Bibliographic Details
Main Author: Lakshtanov, Evgeny L.
Publication Date: 2016
Other Authors: Novikov, Roman G., Vainberg, Boris R.
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/16608
Summary: We develop the Riemann-Hilbert problem approach to in- verse scattering for the two-dimensional Schr odinger equation at xed energy. We obtain global or generic versions of the key results of this approach for the case of positive energy and compactly supported poten- tials. 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.
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spelling A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energyTwo-dimensional inverse scatteringFaddeev functionsGeneralized Riemann-Hilbert-Manakov problemNovikov-Veselov equationWe develop the Riemann-Hilbert problem approach to in- verse scattering for the two-dimensional Schr odinger equation at xed energy. We obtain global or generic versions of the key results of this approach for the case of positive energy and compactly supported poten- tials. 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.Università di Trieste2017-01-09T15:06:31Z2016-12-01T00:00:00Z2016-12info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/16608eng0049-4704Lakshtanov, Evgeny L.Novikov, Roman G.Vainberg, Boris R.info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T03:59:00Zoai:ria.ua.pt:10773/16608Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T13:53:27.486275Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy
title A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy
spellingShingle A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy
Lakshtanov, Evgeny L.
Two-dimensional inverse scattering
Faddeev functions
Generalized Riemann-Hilbert-Manakov problem
Novikov-Veselov equation
title_short A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy
title_full A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy
title_fullStr A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy
title_full_unstemmed A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy
title_sort A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy
author Lakshtanov, Evgeny L.
author_facet Lakshtanov, Evgeny L.
Novikov, Roman G.
Vainberg, Boris R.
author_role author
author2 Novikov, Roman G.
Vainberg, Boris R.
author2_role author
author
dc.contributor.author.fl_str_mv Lakshtanov, Evgeny L.
Novikov, Roman G.
Vainberg, Boris R.
dc.subject.por.fl_str_mv Two-dimensional inverse scattering
Faddeev functions
Generalized Riemann-Hilbert-Manakov problem
Novikov-Veselov equation
topic Two-dimensional inverse scattering
Faddeev functions
Generalized Riemann-Hilbert-Manakov problem
Novikov-Veselov equation
description We develop the Riemann-Hilbert problem approach to in- verse scattering for the two-dimensional Schr odinger equation at xed energy. We obtain global or generic versions of the key results of this approach for the case of positive energy and compactly supported poten- tials. 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.
publishDate 2016
dc.date.none.fl_str_mv 2016-12-01T00:00:00Z
2016-12
2017-01-09T15:06:31Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/16608
url http://hdl.handle.net/10773/16608
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0049-4704
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Università di Trieste
publisher.none.fl_str_mv Università di Trieste
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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