Evolution of Polygonal Lines by the Binormal Flow

The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schrödinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. Finally we prove the existence of a unique solution of the binormal flow with datum...

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Detalles Bibliográficos
Autores: Banica, V., Vega, L.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1345
Acceso en línea:http://hdl.handle.net/20.500.11824/1345
Access Level:acceso abierto
Palabra clave:Binormal flow
Nonlinear Schrödinger equations
Singular data
Talbot effect
Vortex filaments
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spelling Evolution of Polygonal Lines by the Binormal FlowBanica, V.Vega, L.Binormal flowNonlinear Schrödinger equationsSingular dataTalbot effectVortex filamentsThe aim of this paper is threefold. First we display solutions of the cubic nonlinear Schrödinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. Finally we prove the existence of a unique solution of the binormal flow with datum a polygonal line. This equation is used as a model for the vortex filaments dynamics in 3-D fluids and superfluids. We also construct solutions of the binormal flow that present an intermittency phenomena. Finally, the solution we construct for the binormal flow is continued for negative times, yielding a geometric way to approach the continuation after blow-up for the 1-D cubic nonlinear Schrödinger equation.202120212020info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1345reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Inglésinfo:eu-repo/grantAgreement/EC/H2020/669689info:eu-repo/grantAgreement/MINECO//SEV-2017-0718info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/13452026-06-19T12:47:47Z
dc.title.none.fl_str_mv Evolution of Polygonal Lines by the Binormal Flow
title Evolution of Polygonal Lines by the Binormal Flow
spellingShingle Evolution of Polygonal Lines by the Binormal Flow
Banica, V.
Binormal flow
Nonlinear Schrödinger equations
Singular data
Talbot effect
Vortex filaments
title_short Evolution of Polygonal Lines by the Binormal Flow
title_full Evolution of Polygonal Lines by the Binormal Flow
title_fullStr Evolution of Polygonal Lines by the Binormal Flow
title_full_unstemmed Evolution of Polygonal Lines by the Binormal Flow
title_sort Evolution of Polygonal Lines by the Binormal Flow
dc.creator.none.fl_str_mv Banica, V.
Vega, L.
author Banica, V.
author_facet Banica, V.
Vega, L.
author_role author
author2 Vega, L.
author2_role author
dc.subject.none.fl_str_mv Binormal flow
Nonlinear Schrödinger equations
Singular data
Talbot effect
Vortex filaments
topic Binormal flow
Nonlinear Schrödinger equations
Singular data
Talbot effect
Vortex filaments
description The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schrödinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. Finally we prove the existence of a unique solution of the binormal flow with datum a polygonal line. This equation is used as a model for the vortex filaments dynamics in 3-D fluids and superfluids. We also construct solutions of the binormal flow that present an intermittency phenomena. Finally, the solution we construct for the binormal flow is continued for negative times, yielding a geometric way to approach the continuation after blow-up for the 1-D cubic nonlinear Schrödinger equation.
publishDate 2020
dc.date.none.fl_str_mv 2020
2021
2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1345
url http://hdl.handle.net/20.500.11824/1345
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/EC/H2020/669689
info:eu-repo/grantAgreement/MINECO//SEV-2017-0718
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
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dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
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collection BIRD. BCAM's Institutional Repository Data
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