Multibreather and vortex breather stability in Klein–Gordon lattices: equivalence between two different approaches

In this work, we revisit the question of stability of multibreather configurations, i.e. discrete breathers with multiple excited sites at the anti-continuum limit of uncoupled oscillators. We present two methods that yield quantitative predictions about the Floquet multipliers of the linear stabili...

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Autores: Cuevas-Maraver, Jesús, Koukouloyannis, Vassilis, Kevrekidis, Panayotis G., Archilla, Juan F. R.
Tipo de recurso: artículo
Fecha de publicación:2011
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/24841
Acceso en línea:http://hdl.handle.net/11441/24841
https://doi.org/10.1142/S0218127411029690
Access Level:acceso abierto
Palabra clave:Discrete breathers
multibreathers
stability of multibreathers
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spelling Multibreather and vortex breather stability in Klein–Gordon lattices: equivalence between two different approachesCuevas-Maraver, JesúsKoukouloyannis, VassilisKevrekidis, Panayotis G.Archilla, Juan F. R.Discrete breathersmultibreathersstability of multibreathersIn this work, we revisit the question of stability of multibreather configurations, i.e. discrete breathers with multiple excited sites at the anti-continuum limit of uncoupled oscillators. We present two methods that yield quantitative predictions about the Floquet multipliers of the linear stability analysis around such exponentially localized in space, time-periodic orbits, based on the Aubry band method and the MacKay effective Hamiltonian method, and prove that by making the suitable assumptions about the form of the bands in the Aubry band theory, their conclusions are equivalent. Subsequently, we showcase the usefulness of the methods through a series of case examples including one-dimensional multi-breathers, and two-dimensional vortex breathers in the case of a lattice of linearly coupled oscillators with the Morse potential and in that of the discrete φ4 model. © 2011 World Scientific Publishing Company.MICINN project FIS2008-04848Física Aplicada IMinisterio de Ciencia e Innovación (MICIN). España2011info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/24841https://doi.org/10.1142/S0218127411029690reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésInternational Journal of Bifurcation and Chaos, 21(8), 2161-2177http://dx.doi.org/10.1142/S0218127411029690info:eu-repo/semantics/openAccessoai:idus.us.es:11441/248412026-06-17T12:51:07Z
dc.title.none.fl_str_mv Multibreather and vortex breather stability in Klein–Gordon lattices: equivalence between two different approaches
title Multibreather and vortex breather stability in Klein–Gordon lattices: equivalence between two different approaches
spellingShingle Multibreather and vortex breather stability in Klein–Gordon lattices: equivalence between two different approaches
Cuevas-Maraver, Jesús
Discrete breathers
multibreathers
stability of multibreathers
title_short Multibreather and vortex breather stability in Klein–Gordon lattices: equivalence between two different approaches
title_full Multibreather and vortex breather stability in Klein–Gordon lattices: equivalence between two different approaches
title_fullStr Multibreather and vortex breather stability in Klein–Gordon lattices: equivalence between two different approaches
title_full_unstemmed Multibreather and vortex breather stability in Klein–Gordon lattices: equivalence between two different approaches
title_sort Multibreather and vortex breather stability in Klein–Gordon lattices: equivalence between two different approaches
dc.creator.none.fl_str_mv Cuevas-Maraver, Jesús
Koukouloyannis, Vassilis
Kevrekidis, Panayotis G.
Archilla, Juan F. R.
author Cuevas-Maraver, Jesús
author_facet Cuevas-Maraver, Jesús
Koukouloyannis, Vassilis
Kevrekidis, Panayotis G.
Archilla, Juan F. R.
author_role author
author2 Koukouloyannis, Vassilis
Kevrekidis, Panayotis G.
Archilla, Juan F. R.
author2_role author
author
author
dc.contributor.none.fl_str_mv Física Aplicada I
Ministerio de Ciencia e Innovación (MICIN). España
dc.subject.none.fl_str_mv Discrete breathers
multibreathers
stability of multibreathers
topic Discrete breathers
multibreathers
stability of multibreathers
description In this work, we revisit the question of stability of multibreather configurations, i.e. discrete breathers with multiple excited sites at the anti-continuum limit of uncoupled oscillators. We present two methods that yield quantitative predictions about the Floquet multipliers of the linear stability analysis around such exponentially localized in space, time-periodic orbits, based on the Aubry band method and the MacKay effective Hamiltonian method, and prove that by making the suitable assumptions about the form of the bands in the Aubry band theory, their conclusions are equivalent. Subsequently, we showcase the usefulness of the methods through a series of case examples including one-dimensional multi-breathers, and two-dimensional vortex breathers in the case of a lattice of linearly coupled oscillators with the Morse potential and in that of the discrete φ4 model. © 2011 World Scientific Publishing Company.
publishDate 2011
dc.date.none.fl_str_mv 2011
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/24841
https://doi.org/10.1142/S0218127411029690
url http://hdl.handle.net/11441/24841
https://doi.org/10.1142/S0218127411029690
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv International Journal of Bifurcation and Chaos, 21(8), 2161-2177
http://dx.doi.org/10.1142/S0218127411029690
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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