PT-Symmetric dimer in a generalized model of coupled nonlinear oscillators

In the present work, we explore the case of a general PT -symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave approximation converting it into a discrete nonlinear Schr¨odinger...

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Autores: Cuevas-Maraver, Jesús, Khare, Avinash, Kevrekidis, Panayotis G., Xu, Haitao, Saxena, Avadh
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2015
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/32000
Acceso en línea:http://hdl.handle.net/11441/32000
https://doi.org/10.1007/s10773-014-2429-6
Access Level:acceso abierto
Palabra clave:Oscillators
PT-symmetry
Stability
Periodic orbits
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spelling PT-Symmetric dimer in a generalized model of coupled nonlinear oscillatorsCuevas-Maraver, JesúsKhare, AvinashKevrekidis, Panayotis G.Xu, HaitaoSaxena, AvadhOscillatorsPT-symmetryStabilityPeriodic orbitsIn the present work, we explore the case of a general PT -symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave approximation converting it into a discrete nonlinear Schr¨odinger type dimer. In the latter context, the stationary solutions and their stability are identified numerically but also wherever possible analytically. Solutions stemming from both symmetric and anti-symmetric special limits are identified. A number of special cases are explored regarding the ratio of coefficients of nonlinearity between oscillators over the intrinsic one of each oscillator. Finally, the considerations are extended to the original oscillator model, where periodic orbits and their stability are obtained. When the solutions are found to be unstable their dynamics is monitored by means of direct numerical simulations.SpringerFísica Aplicada I2015info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/32000https://doi.org/10.1007/s10773-014-2429-6reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésInternational Journal of Theoretical Physics, 54 (11), 3960-3985.http://dx.doi.org/10.1007/s10773-014-2429-6info:eu-repo/semantics/openAccessoai:idus.us.es:11441/320002026-06-17T12:51:07Z
dc.title.none.fl_str_mv PT-Symmetric dimer in a generalized model of coupled nonlinear oscillators
title PT-Symmetric dimer in a generalized model of coupled nonlinear oscillators
spellingShingle PT-Symmetric dimer in a generalized model of coupled nonlinear oscillators
Cuevas-Maraver, Jesús
Oscillators
PT-symmetry
Stability
Periodic orbits
title_short PT-Symmetric dimer in a generalized model of coupled nonlinear oscillators
title_full PT-Symmetric dimer in a generalized model of coupled nonlinear oscillators
title_fullStr PT-Symmetric dimer in a generalized model of coupled nonlinear oscillators
title_full_unstemmed PT-Symmetric dimer in a generalized model of coupled nonlinear oscillators
title_sort PT-Symmetric dimer in a generalized model of coupled nonlinear oscillators
dc.creator.none.fl_str_mv Cuevas-Maraver, Jesús
Khare, Avinash
Kevrekidis, Panayotis G.
Xu, Haitao
Saxena, Avadh
author Cuevas-Maraver, Jesús
author_facet Cuevas-Maraver, Jesús
Khare, Avinash
Kevrekidis, Panayotis G.
Xu, Haitao
Saxena, Avadh
author_role author
author2 Khare, Avinash
Kevrekidis, Panayotis G.
Xu, Haitao
Saxena, Avadh
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Física Aplicada I
dc.subject.none.fl_str_mv Oscillators
PT-symmetry
Stability
Periodic orbits
topic Oscillators
PT-symmetry
Stability
Periodic orbits
description In the present work, we explore the case of a general PT -symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave approximation converting it into a discrete nonlinear Schr¨odinger type dimer. In the latter context, the stationary solutions and their stability are identified numerically but also wherever possible analytically. Solutions stemming from both symmetric and anti-symmetric special limits are identified. A number of special cases are explored regarding the ratio of coefficients of nonlinearity between oscillators over the intrinsic one of each oscillator. Finally, the considerations are extended to the original oscillator model, where periodic orbits and their stability are obtained. When the solutions are found to be unstable their dynamics is monitored by means of direct numerical simulations.
publishDate 2015
dc.date.none.fl_str_mv 2015
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/32000
https://doi.org/10.1007/s10773-014-2429-6
url http://hdl.handle.net/11441/32000
https://doi.org/10.1007/s10773-014-2429-6
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv International Journal of Theoretical Physics, 54 (11), 3960-3985.
http://dx.doi.org/10.1007/s10773-014-2429-6
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 Springer
publisher.none.fl_str_mv Springer
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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