Optical solitons in nematic liquid crystals: Model with saturation effects

Autores
Borgna, Juan Pablo; Panayotaros, Panayotis; Rial, Diego Fernando; Sanchez Fernandez de la Vega, Constanza Mariel
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study a 2D system that couples a Schrödinger evolution equation to a nonlinear elliptic equation and models the propagation of a laser beam in a nematic liquid crystal. The nonlinear elliptic equation describes the response of the director angle to the laser beam electric field. We obtain results on well-posedness and solitary wave solutions of this system, generalizing results for a well-studied simpler system with a linear elliptic equation for the director field. The analysis of the nonlinear elliptic problem shows the existence of an isolated global branch of solutions with director angles that remain bounded for arbitrary electric field. The results on the director equation are also used to show local and global existence, as well as decay for initial conditions with sufficiently small L 2-norm. For sufficiently large L 2-norm we show the existence of energy minimizing optical solitons with radial, positive and monotone profiles.
Fil: Borgna, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de San Martín; Argentina
Fil: Panayotaros, Panayotis. Universidad Nacional Autónoma de México; México
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
Fil: Sanchez Fernandez de la Vega, Constanza Mariel. 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
NEMATIC LIQUID CRYSTALS
NONLINEAR SCHRODINGER EQUATIONS
OPTICAL 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:11336/93643
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Optical solitons in nematic liquid crystals: Model with saturation effectsBorgna, Juan PabloPanayotaros, PanayotisRial, Diego FernandoSanchez Fernandez de la Vega, Constanza MarielNEMATIC LIQUID CRYSTALSNONLINEAR SCHRODINGER EQUATIONSOPTICAL SOLITONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study a 2D system that couples a Schrödinger evolution equation to a nonlinear elliptic equation and models the propagation of a laser beam in a nematic liquid crystal. The nonlinear elliptic equation describes the response of the director angle to the laser beam electric field. We obtain results on well-posedness and solitary wave solutions of this system, generalizing results for a well-studied simpler system with a linear elliptic equation for the director field. The analysis of the nonlinear elliptic problem shows the existence of an isolated global branch of solutions with director angles that remain bounded for arbitrary electric field. The results on the director equation are also used to show local and global existence, as well as decay for initial conditions with sufficiently small L 2-norm. For sufficiently large L 2-norm we show the existence of energy minimizing optical solitons with radial, positive and monotone profiles.Fil: Borgna, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de San Martín; ArgentinaFil: Panayotaros, Panayotis. Universidad Nacional Autónoma de México; MéxicoFil: 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"; ArgentinaFil: Sanchez Fernandez de la Vega, Constanza Mariel. 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"; ArgentinaIOP Publishing2018-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/93643Borgna, Juan Pablo; Panayotaros, Panayotis; Rial, Diego Fernando; Sanchez Fernandez de la Vega, Constanza Mariel; Optical solitons in nematic liquid crystals: Model with saturation effects; IOP Publishing; Nonlinearity; 31; 4; 4-2018; 1535-15590951-7715CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/1361-6544/aaa2e2info:eu-repo/semantics/altIdentifier/doi/10.1088/1361-6544/aaa2e2info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:53:15Zoai:ri.conicet.gov.ar:11336/93643instacron: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:34982025-09-03 09:53:15.882CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Optical solitons in nematic liquid crystals: Model with saturation effects
title Optical solitons in nematic liquid crystals: Model with saturation effects
spellingShingle Optical solitons in nematic liquid crystals: Model with saturation effects
Borgna, Juan Pablo
NEMATIC LIQUID CRYSTALS
NONLINEAR SCHRODINGER EQUATIONS
OPTICAL SOLITONS
title_short Optical solitons in nematic liquid crystals: Model with saturation effects
title_full Optical solitons in nematic liquid crystals: Model with saturation effects
title_fullStr Optical solitons in nematic liquid crystals: Model with saturation effects
title_full_unstemmed Optical solitons in nematic liquid crystals: Model with saturation effects
title_sort Optical solitons in nematic liquid crystals: Model with saturation effects
dc.creator.none.fl_str_mv Borgna, Juan Pablo
Panayotaros, Panayotis
Rial, Diego Fernando
Sanchez Fernandez de la Vega, Constanza Mariel
author Borgna, Juan Pablo
author_facet Borgna, Juan Pablo
Panayotaros, Panayotis
Rial, Diego Fernando
Sanchez Fernandez de la Vega, Constanza Mariel
author_role author
author2 Panayotaros, Panayotis
Rial, Diego Fernando
Sanchez Fernandez de la Vega, Constanza Mariel
author2_role author
author
author
dc.subject.none.fl_str_mv NEMATIC LIQUID CRYSTALS
NONLINEAR SCHRODINGER EQUATIONS
OPTICAL SOLITONS
topic NEMATIC LIQUID CRYSTALS
NONLINEAR SCHRODINGER EQUATIONS
OPTICAL SOLITONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study a 2D system that couples a Schrödinger evolution equation to a nonlinear elliptic equation and models the propagation of a laser beam in a nematic liquid crystal. The nonlinear elliptic equation describes the response of the director angle to the laser beam electric field. We obtain results on well-posedness and solitary wave solutions of this system, generalizing results for a well-studied simpler system with a linear elliptic equation for the director field. The analysis of the nonlinear elliptic problem shows the existence of an isolated global branch of solutions with director angles that remain bounded for arbitrary electric field. The results on the director equation are also used to show local and global existence, as well as decay for initial conditions with sufficiently small L 2-norm. For sufficiently large L 2-norm we show the existence of energy minimizing optical solitons with radial, positive and monotone profiles.
Fil: Borgna, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de San Martín; Argentina
Fil: Panayotaros, Panayotis. Universidad Nacional Autónoma de México; México
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
Fil: Sanchez Fernandez de la Vega, Constanza Mariel. 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 We study a 2D system that couples a Schrödinger evolution equation to a nonlinear elliptic equation and models the propagation of a laser beam in a nematic liquid crystal. The nonlinear elliptic equation describes the response of the director angle to the laser beam electric field. We obtain results on well-posedness and solitary wave solutions of this system, generalizing results for a well-studied simpler system with a linear elliptic equation for the director field. The analysis of the nonlinear elliptic problem shows the existence of an isolated global branch of solutions with director angles that remain bounded for arbitrary electric field. The results on the director equation are also used to show local and global existence, as well as decay for initial conditions with sufficiently small L 2-norm. For sufficiently large L 2-norm we show the existence of energy minimizing optical solitons with radial, positive and monotone profiles.
publishDate 2018
dc.date.none.fl_str_mv 2018-04
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/11336/93643
Borgna, Juan Pablo; Panayotaros, Panayotis; Rial, Diego Fernando; Sanchez Fernandez de la Vega, Constanza Mariel; Optical solitons in nematic liquid crystals: Model with saturation effects; IOP Publishing; Nonlinearity; 31; 4; 4-2018; 1535-1559
0951-7715
CONICET Digital
CONICET
url http://hdl.handle.net/11336/93643
identifier_str_mv Borgna, Juan Pablo; Panayotaros, Panayotis; Rial, Diego Fernando; Sanchez Fernandez de la Vega, Constanza Mariel; Optical solitons in nematic liquid crystals: Model with saturation effects; IOP Publishing; Nonlinearity; 31; 4; 4-2018; 1535-1559
0951-7715
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/1361-6544/aaa2e2
info:eu-repo/semantics/altIdentifier/doi/10.1088/1361-6544/aaa2e2
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
application/pdf
application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
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
_version_ 1842269212027912192
score 13.13397

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