Self-similar solutions with compactly supported profile of some nonlinear Schrödinger equations

“Sharp localized” solutions (i.e. with compact support for each given time t) of a singular nonlinear type Schrödinger equation in the whole space R N are constructed here under the assumption that they have a self-similar structure. It requires the assumption that the external forcing term satisfie...

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Detalles Bibliográficos
Autores: Bègout, Pascal, Díaz Díaz, Jesús Ildefonso
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/33950
Acceso en línea:https://hdl.handle.net/20.500.14352/33950
Access Level:acceso abierto
Palabra clave:517.9
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
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spelling Self-similar solutions with compactly supported profile of some nonlinear Schrödinger equationsBègout, PascalDíaz Díaz, Jesús Ildefonso517.9Ecuaciones diferenciales1202.07 Ecuaciones en Diferencias“Sharp localized” solutions (i.e. with compact support for each given time t) of a singular nonlinear type Schrödinger equation in the whole space R N are constructed here under the assumption that they have a self-similar structure. It requires the assumption that the external forcing term satisfies that f(t, x) = t−(p−2)/2F (t−1/2x) for some complex exponent p and for some profile function F which is assumed to be with compact support in R N . We show the existence of solutions of the form u(t, x) = t p/2U(t−1/2x), with a profile U, which also has compact support in R N . The proof of the localization of the support of the profile U uses some suitable energy method applied to the stationary problem satisfied by U after some unknown transformation.Department of Mathematics Texas State UniversityUniversidad Complutense de Madrid20142014-01-0120142014-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/33950reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/339502026-06-02T12:44:21Z
dc.title.none.fl_str_mv Self-similar solutions with compactly supported profile of some nonlinear Schrödinger equations
title Self-similar solutions with compactly supported profile of some nonlinear Schrödinger equations
spellingShingle Self-similar solutions with compactly supported profile of some nonlinear Schrödinger equations
Bègout, Pascal
517.9
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
title_short Self-similar solutions with compactly supported profile of some nonlinear Schrödinger equations
title_full Self-similar solutions with compactly supported profile of some nonlinear Schrödinger equations
title_fullStr Self-similar solutions with compactly supported profile of some nonlinear Schrödinger equations
title_full_unstemmed Self-similar solutions with compactly supported profile of some nonlinear Schrödinger equations
title_sort Self-similar solutions with compactly supported profile of some nonlinear Schrödinger equations
dc.creator.none.fl_str_mv Bègout, Pascal
Díaz Díaz, Jesús Ildefonso
author Bègout, Pascal
author_facet Bègout, Pascal
Díaz Díaz, Jesús Ildefonso
author_role author
author2 Díaz Díaz, Jesús Ildefonso
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 517.9
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
topic 517.9
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
description “Sharp localized” solutions (i.e. with compact support for each given time t) of a singular nonlinear type Schrödinger equation in the whole space R N are constructed here under the assumption that they have a self-similar structure. It requires the assumption that the external forcing term satisfies that f(t, x) = t−(p−2)/2F (t−1/2x) for some complex exponent p and for some profile function F which is assumed to be with compact support in R N . We show the existence of solutions of the form u(t, x) = t p/2U(t−1/2x), with a profile U, which also has compact support in R N . The proof of the localization of the support of the profile U uses some suitable energy method applied to the stationary problem satisfied by U after some unknown transformation.
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-01-01
2014
2014-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/33950
url https://hdl.handle.net/20.500.14352/33950
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Department of Mathematics Texas State University
publisher.none.fl_str_mv Department of Mathematics Texas State University
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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