Chaos and Intermittency in the DNLS Equation Describing the Parallel Alfvén Wave Propagation

Autores
Krause, Gustavo Javier; Elaskar, Sergio Amado; Costa, Andrea
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
When the Hall effect is included in the magnetohydrodynamics equations (Hall-MHD model) the wave propagation modes become coupled, but for propagation parallel to the ambient magnetic field the Alfvén mode decouples from the magnetosonic ones, resulting in circularly polarized waves that are described by the derivative nonlinear Schrödinger (DNLS) equation. In this paper, the DNLS equation is numerically solved using spectral methods for the spatial derivatives and a fourth order Runge-Kutta scheme for time integration. Firstly, the nondiffusive DNLS equation is considered to test the validity of the method by verifying the analytical condition of modulational stability. Later, diffusive and excitatory effects are incorporated to compare the numerical results with those obtained by a three-wave truncation model. The results show that different types of attractors can exist depending on the diffusion level: for relatively large damping, there are fixed points for which the truncation model is a good approximation; for low damping, chaotic solutions appear and the three-wave truncation model fails due to the emergence of new nonnegligible modes.
Fil: Krause, Gustavo Javier. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Departamento de Aeronáutica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Elaskar, Sergio Amado. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Departamento de Aeronáutica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Costa, Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomia Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomia Teórica y Experimental; Argentina
Materia
DNLS EQUATION
SPECTRAL METHODS
TRUNCATION METHOD
ALFVÉN WAVES
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:11336/32257
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/32257
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Chaos and Intermittency in the DNLS Equation Describing the Parallel Alfvén Wave PropagationKrause, Gustavo JavierElaskar, Sergio AmadoCosta, AndreaDNLS EQUATIONSPECTRAL METHODSTRUNCATION METHODALFVÉN WAVEShttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1When the Hall effect is included in the magnetohydrodynamics equations (Hall-MHD model) the wave propagation modes become coupled, but for propagation parallel to the ambient magnetic field the Alfvén mode decouples from the magnetosonic ones, resulting in circularly polarized waves that are described by the derivative nonlinear Schrödinger (DNLS) equation. In this paper, the DNLS equation is numerically solved using spectral methods for the spatial derivatives and a fourth order Runge-Kutta scheme for time integration. Firstly, the nondiffusive DNLS equation is considered to test the validity of the method by verifying the analytical condition of modulational stability. Later, diffusive and excitatory effects are incorporated to compare the numerical results with those obtained by a three-wave truncation model. The results show that different types of attractors can exist depending on the diffusion level: for relatively large damping, there are fixed points for which the truncation model is a good approximation; for low damping, chaotic solutions appear and the three-wave truncation model fails due to the emergence of new nonnegligible modes.Fil: Krause, Gustavo Javier. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Departamento de Aeronáutica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Elaskar, Sergio Amado. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Departamento de Aeronáutica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Costa, Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomia Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomia Teórica y Experimental; ArgentinaHindawi Publishing Corporation2014-04info: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/11336/32257Costa, Andrea; Elaskar, Sergio Amado; Krause, Gustavo Javier; Chaos and Intermittency in the DNLS Equation Describing the Parallel Alfvén Wave Propagation; Hindawi Publishing Corporation; Journal of Astrophysics; 2014; 4-2014; 1-15; 8120522356-718XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1155/2014/812052info:eu-repo/semantics/altIdentifier/url/https://www.hindawi.com/journals/jas/2014/812052/info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:07:13Zoai:ri.conicet.gov.ar:11336/32257instacron: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 10:07:13.639CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Chaos and Intermittency in the DNLS Equation Describing the Parallel Alfvén Wave Propagation
title Chaos and Intermittency in the DNLS Equation Describing the Parallel Alfvén Wave Propagation
spellingShingle Chaos and Intermittency in the DNLS Equation Describing the Parallel Alfvén Wave Propagation
Krause, Gustavo Javier
DNLS EQUATION
SPECTRAL METHODS
TRUNCATION METHOD
ALFVÉN WAVES
title_short Chaos and Intermittency in the DNLS Equation Describing the Parallel Alfvén Wave Propagation
title_full Chaos and Intermittency in the DNLS Equation Describing the Parallel Alfvén Wave Propagation
title_fullStr Chaos and Intermittency in the DNLS Equation Describing the Parallel Alfvén Wave Propagation
title_full_unstemmed Chaos and Intermittency in the DNLS Equation Describing the Parallel Alfvén Wave Propagation
title_sort Chaos and Intermittency in the DNLS Equation Describing the Parallel Alfvén Wave Propagation
dc.creator.none.fl_str_mv Krause, Gustavo Javier
Elaskar, Sergio Amado
Costa, Andrea
author Krause, Gustavo Javier
author_facet Krause, Gustavo Javier
Elaskar, Sergio Amado
Costa, Andrea
author_role author
author2 Elaskar, Sergio Amado
Costa, Andrea
author2_role author
author
dc.subject.none.fl_str_mv DNLS EQUATION
SPECTRAL METHODS
TRUNCATION METHOD
ALFVÉN WAVES
topic DNLS EQUATION
SPECTRAL METHODS
TRUNCATION METHOD
ALFVÉN WAVES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv When the Hall effect is included in the magnetohydrodynamics equations (Hall-MHD model) the wave propagation modes become coupled, but for propagation parallel to the ambient magnetic field the Alfvén mode decouples from the magnetosonic ones, resulting in circularly polarized waves that are described by the derivative nonlinear Schrödinger (DNLS) equation. In this paper, the DNLS equation is numerically solved using spectral methods for the spatial derivatives and a fourth order Runge-Kutta scheme for time integration. Firstly, the nondiffusive DNLS equation is considered to test the validity of the method by verifying the analytical condition of modulational stability. Later, diffusive and excitatory effects are incorporated to compare the numerical results with those obtained by a three-wave truncation model. The results show that different types of attractors can exist depending on the diffusion level: for relatively large damping, there are fixed points for which the truncation model is a good approximation; for low damping, chaotic solutions appear and the three-wave truncation model fails due to the emergence of new nonnegligible modes.
Fil: Krause, Gustavo Javier. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Departamento de Aeronáutica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Elaskar, Sergio Amado. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Departamento de Aeronáutica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Costa, Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomia Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomia Teórica y Experimental; Argentina
description When the Hall effect is included in the magnetohydrodynamics equations (Hall-MHD model) the wave propagation modes become coupled, but for propagation parallel to the ambient magnetic field the Alfvén mode decouples from the magnetosonic ones, resulting in circularly polarized waves that are described by the derivative nonlinear Schrödinger (DNLS) equation. In this paper, the DNLS equation is numerically solved using spectral methods for the spatial derivatives and a fourth order Runge-Kutta scheme for time integration. Firstly, the nondiffusive DNLS equation is considered to test the validity of the method by verifying the analytical condition of modulational stability. Later, diffusive and excitatory effects are incorporated to compare the numerical results with those obtained by a three-wave truncation model. The results show that different types of attractors can exist depending on the diffusion level: for relatively large damping, there are fixed points for which the truncation model is a good approximation; for low damping, chaotic solutions appear and the three-wave truncation model fails due to the emergence of new nonnegligible modes.
publishDate 2014
dc.date.none.fl_str_mv 2014-04
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/11336/32257
Costa, Andrea; Elaskar, Sergio Amado; Krause, Gustavo Javier; Chaos and Intermittency in the DNLS Equation Describing the Parallel Alfvén Wave Propagation; Hindawi Publishing Corporation; Journal of Astrophysics; 2014; 4-2014; 1-15; 812052
2356-718X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/32257
identifier_str_mv Costa, Andrea; Elaskar, Sergio Amado; Krause, Gustavo Javier; Chaos and Intermittency in the DNLS Equation Describing the Parallel Alfvén Wave Propagation; Hindawi Publishing Corporation; Journal of Astrophysics; 2014; 4-2014; 1-15; 812052
2356-718X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1155/2014/812052
info:eu-repo/semantics/altIdentifier/url/https://www.hindawi.com/journals/jas/2014/812052/
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 Hindawi Publishing Corporation
publisher.none.fl_str_mv Hindawi Publishing Corporation
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 13.13397

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