Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation

We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de Vries equation, through a fixed point argument in weighted $W^{1,\infty}$ around a carefully chosen, two term ansatz. Such knowledge is crucial in the study of stability properties of the self-simi...

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Detalles Bibliográficos
Autores: Correia, S., Côte, R., Vega, L.
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2018
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/831
Acceso en línea:http://hdl.handle.net/20.500.11824/831
Access Level:acceso abierto
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spelling Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equationCorreia, S.Côte, R.Vega, L.We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de Vries equation, through a fixed point argument in weighted $W^{1,\infty}$ around a carefully chosen, two term ansatz. Such knowledge is crucial in the study of stability properties of the self-similar solutions for the modified Korteweg-de Vries flow. In the defocusing case, the self-similar profiles are solutions to the PainlevéII equation. Although they were extensively studied in physical space, no result to our knowledge describe their behavior in Fourier space. We are able to relate the constants involved in the description in Fourier space with those involved in the description in physical space.201820182018info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/831reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://arxiv.org/abs/1807.02302info:eu-repo/grantAgreement/EC/H2020/669689info:eu-repo/grantAgreement/MINECO//SEV-2013-0323info:eu-repo/grantAgreement/MINECO//MTM2014-53850-Pinfo:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2014-2017Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/8312026-06-19T12:47:47Z
dc.title.none.fl_str_mv Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation
title Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation
spellingShingle Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation
Correia, S.
title_short Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation
title_full Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation
title_fullStr Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation
title_full_unstemmed Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation
title_sort Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation
dc.creator.none.fl_str_mv Correia, S.
Côte, R.
Vega, L.
author Correia, S.
author_facet Correia, S.
Côte, R.
Vega, L.
author_role author
author2 Côte, R.
Vega, L.
author2_role author
author
description We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de Vries equation, through a fixed point argument in weighted $W^{1,\infty}$ around a carefully chosen, two term ansatz. Such knowledge is crucial in the study of stability properties of the self-similar solutions for the modified Korteweg-de Vries flow. In the defocusing case, the self-similar profiles are solutions to the PainlevéII equation. Although they were extensively studied in physical space, no result to our knowledge describe their behavior in Fourier space. We are able to relate the constants involved in the description in Fourier space with those involved in the description in physical space.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018
2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
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format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/831
url http://hdl.handle.net/20.500.11824/831
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://arxiv.org/abs/1807.02302
info:eu-repo/grantAgreement/EC/H2020/669689
info:eu-repo/grantAgreement/MINECO//SEV-2013-0323
info:eu-repo/grantAgreement/MINECO//MTM2014-53850-P
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2014-2017
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
dc.format.none.fl_str_mv application/pdf
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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