Existence of ground states for a one-dimensional relativistic schrödinger equation

Autores
Borgna, Juan Pablo; Rial, Diego Fernando
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Relativistic Schrödinger equation with a nonlinear potential interaction describes the dynamics of a particle, with rest mass m, travelling to a significant fraction |v| < 1 of the light speed c = 1. At first, we deal with the local and global existence of solutions of the flux, and in the second term, and according to the relativistic nature of the problem, we look for boosted solitons as ψ(x, t) = eiμtφv(x - vt), where the profile φ v ∈ H 1/2 (R{double-struck}) is a minimizer of a suitable variational problem. Our proof uses a concentration-compactness-type argument. Stability results for the boosted solitons are established.
Fil: Borgna, Juan Pablo. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Rial, Diego Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
GROUND STATES
NONLINEAR EQUATION
SCHROEDINGER EQUATION
SOLITONS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/125772
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Existence of ground states for a one-dimensional relativistic schrödinger equationBorgna, Juan PabloRial, Diego FernandoGROUND STATESNONLINEAR EQUATIONSCHROEDINGER EQUATIONSOLITONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Relativistic Schrödinger equation with a nonlinear potential interaction describes the dynamics of a particle, with rest mass m, travelling to a significant fraction |v| < 1 of the light speed c = 1. At first, we deal with the local and global existence of solutions of the flux, and in the second term, and according to the relativistic nature of the problem, we look for boosted solitons as ψ(x, t) = eiμtφv(x - vt), where the profile φ v ∈ H 1/2 (R{double-struck}) is a minimizer of a suitable variational problem. Our proof uses a concentration-compactness-type argument. Stability results for the boosted solitons are established.Fil: Borgna, Juan Pablo. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Rial, Diego Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaAmerican Institute of Physics2012-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/125772Borgna, Juan Pablo; Rial, Diego Fernando; Existence of ground states for a one-dimensional relativistic schrödinger equation; American Institute of Physics; Journal of Mathematical Physics; 53; 6; 6-2012; 1-190022-2488CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1063/1.4726198info:eu-repo/semantics/altIdentifier/url/https://aip.scitation.org/doi/10.1063/1.4726198info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:36:13Zoai:ri.conicet.gov.ar:11336/125772instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:36:13.296CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Existence of ground states for a one-dimensional relativistic schrödinger equation
title Existence of ground states for a one-dimensional relativistic schrödinger equation
spellingShingle Existence of ground states for a one-dimensional relativistic schrödinger equation
Borgna, Juan Pablo
GROUND STATES
NONLINEAR EQUATION
SCHROEDINGER EQUATION
SOLITONS
title_short Existence of ground states for a one-dimensional relativistic schrödinger equation
title_full Existence of ground states for a one-dimensional relativistic schrödinger equation
title_fullStr Existence of ground states for a one-dimensional relativistic schrödinger equation
title_full_unstemmed Existence of ground states for a one-dimensional relativistic schrödinger equation
title_sort Existence of ground states for a one-dimensional relativistic schrödinger equation
dc.creator.none.fl_str_mv Borgna, Juan Pablo
Rial, Diego Fernando
author Borgna, Juan Pablo
author_facet Borgna, Juan Pablo
Rial, Diego Fernando
author_role author
author2 Rial, Diego Fernando
author2_role author
dc.subject.none.fl_str_mv GROUND STATES
NONLINEAR EQUATION
SCHROEDINGER EQUATION
SOLITONS
topic GROUND STATES
NONLINEAR EQUATION
SCHROEDINGER EQUATION
SOLITONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Relativistic Schrödinger equation with a nonlinear potential interaction describes the dynamics of a particle, with rest mass m, travelling to a significant fraction |v| < 1 of the light speed c = 1. At first, we deal with the local and global existence of solutions of the flux, and in the second term, and according to the relativistic nature of the problem, we look for boosted solitons as ψ(x, t) = eiμtφv(x - vt), where the profile φ v ∈ H 1/2 (R{double-struck}) is a minimizer of a suitable variational problem. Our proof uses a concentration-compactness-type argument. Stability results for the boosted solitons are established.
Fil: Borgna, Juan Pablo. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Rial, Diego Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description Relativistic Schrödinger equation with a nonlinear potential interaction describes the dynamics of a particle, with rest mass m, travelling to a significant fraction |v| < 1 of the light speed c = 1. At first, we deal with the local and global existence of solutions of the flux, and in the second term, and according to the relativistic nature of the problem, we look for boosted solitons as ψ(x, t) = eiμtφv(x - vt), where the profile φ v ∈ H 1/2 (R{double-struck}) is a minimizer of a suitable variational problem. Our proof uses a concentration-compactness-type argument. Stability results for the boosted solitons are established.
publishDate 2012
dc.date.none.fl_str_mv 2012-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/125772
Borgna, Juan Pablo; Rial, Diego Fernando; Existence of ground states for a one-dimensional relativistic schrödinger equation; American Institute of Physics; Journal of Mathematical Physics; 53; 6; 6-2012; 1-19
0022-2488
CONICET Digital
CONICET
url http://hdl.handle.net/11336/125772
identifier_str_mv Borgna, Juan Pablo; Rial, Diego Fernando; Existence of ground states for a one-dimensional relativistic schrödinger equation; American Institute of Physics; Journal of Mathematical Physics; 53; 6; 6-2012; 1-19
0022-2488
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1063/1.4726198
info:eu-repo/semantics/altIdentifier/url/https://aip.scitation.org/doi/10.1063/1.4726198
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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