Stability of Breathers for a Periodic Klein–Gordon Equation

The existence of breather-type solutions, i.e., solutions that are periodic in time and exponentially localized in space, is a very unusual feature for continuum, nonlinear wave-type equations. Following an earlier work establishing a theorem for the existence of such structures, we bring to bear a...

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Autores: Chirilus-Bruckner, Martina, Cuevas-Maraver, Jesús, Kevrekidis, Panayotis G.
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/163539
Acesso em linha:https://hdl.handle.net/11441/163539
https://doi.org/10.3390/e26090756
Access Level:acceso abierto
Palavra-chave:Nonlinear Klein-Gordon PDE
Spectral stability
Breathers
Heterogeneous media
Center manifold reduction
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spelling Stability of Breathers for a Periodic Klein–Gordon EquationChirilus-Bruckner, MartinaCuevas-Maraver, JesúsKevrekidis, Panayotis G.Nonlinear Klein-Gordon PDESpectral stabilityBreathersHeterogeneous mediaCenter manifold reductionThe existence of breather-type solutions, i.e., solutions that are periodic in time and exponentially localized in space, is a very unusual feature for continuum, nonlinear wave-type equations. Following an earlier work establishing a theorem for the existence of such structures, we bring to bear a combination of analysis-inspired numerical tools that permit the construction of such waveforms to a desired numerical accuracy. In addition, this enables us to explore their numerical stability. Our computations show that for the spatially heterogeneous form of the ϕ4 model considered herein, the breather solutions are generically unstable. Their instability seems to generically favor the motion of the relevant structures. We expect that these results may inspire further studies towards the identification of stable continuous breathers in spatially heterogeneous, continuum nonlinear wave equation models.MDPIFísica Aplicada IFQM280: Física no Lineal2024info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/163539https://doi.org/10.3390/e26090756reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)Ingléshttps://www.mdpi.com/1099-4300/26/9/756info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1635392026-06-17T12:51:07Z
dc.title.none.fl_str_mv Stability of Breathers for a Periodic Klein–Gordon Equation
title Stability of Breathers for a Periodic Klein–Gordon Equation
spellingShingle Stability of Breathers for a Periodic Klein–Gordon Equation
Chirilus-Bruckner, Martina
Nonlinear Klein-Gordon PDE
Spectral stability
Breathers
Heterogeneous media
Center manifold reduction
title_short Stability of Breathers for a Periodic Klein–Gordon Equation
title_full Stability of Breathers for a Periodic Klein–Gordon Equation
title_fullStr Stability of Breathers for a Periodic Klein–Gordon Equation
title_full_unstemmed Stability of Breathers for a Periodic Klein–Gordon Equation
title_sort Stability of Breathers for a Periodic Klein–Gordon Equation
dc.creator.none.fl_str_mv Chirilus-Bruckner, Martina
Cuevas-Maraver, Jesús
Kevrekidis, Panayotis G.
author Chirilus-Bruckner, Martina
author_facet Chirilus-Bruckner, Martina
Cuevas-Maraver, Jesús
Kevrekidis, Panayotis G.
author_role author
author2 Cuevas-Maraver, Jesús
Kevrekidis, Panayotis G.
author2_role author
author
dc.contributor.none.fl_str_mv Física Aplicada I
FQM280: Física no Lineal
dc.subject.none.fl_str_mv Nonlinear Klein-Gordon PDE
Spectral stability
Breathers
Heterogeneous media
Center manifold reduction
topic Nonlinear Klein-Gordon PDE
Spectral stability
Breathers
Heterogeneous media
Center manifold reduction
description The existence of breather-type solutions, i.e., solutions that are periodic in time and exponentially localized in space, is a very unusual feature for continuum, nonlinear wave-type equations. Following an earlier work establishing a theorem for the existence of such structures, we bring to bear a combination of analysis-inspired numerical tools that permit the construction of such waveforms to a desired numerical accuracy. In addition, this enables us to explore their numerical stability. Our computations show that for the spatially heterogeneous form of the ϕ4 model considered herein, the breather solutions are generically unstable. Their instability seems to generically favor the motion of the relevant structures. We expect that these results may inspire further studies towards the identification of stable continuous breathers in spatially heterogeneous, continuum nonlinear wave equation models.
publishDate 2024
dc.date.none.fl_str_mv 2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/163539
https://doi.org/10.3390/e26090756
url https://hdl.handle.net/11441/163539
https://doi.org/10.3390/e26090756
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://www.mdpi.com/1099-4300/26/9/756
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.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
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
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score 15,812455

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