Dissipative Localised Structures for the Complex Discrete Ginzburg–Landau Equation

The discrete complex Ginzburg–Landau equation is a fundamental model for the dynamics of nonlinear lattices incorporating competitive dissipation and energy gain effects. Such mechanisms are of particular importance for the study of survival/destruction of localised structures in many physical situa...

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Authors: Hennig, Dirk, Karachalios, Nikos I., Cuevas-Maraver, Jesús
Format: article
Status:Versión enviada para evaluación y publicación
Publication Date:2023
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/145357
Online Access:https://hdl.handle.net/11441/145357
https://doi.org/10.1007/s00332-023-09904-2
Access Level:Open access
Keyword:Discrete Ginzburg-Landau equation
Ablowitz-Ladik equation
Discrete Nonlinear Schrödinger equations
Dissipative solitons
Persistence
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spelling Dissipative Localised Structures for the Complex Discrete Ginzburg–Landau EquationHennig, DirkKarachalios, Nikos I.Cuevas-Maraver, JesúsDiscrete Ginzburg-Landau equationAblowitz-Ladik equationDiscrete Nonlinear Schrödinger equationsDissipative solitonsPersistenceThe discrete complex Ginzburg–Landau equation is a fundamental model for the dynamics of nonlinear lattices incorporating competitive dissipation and energy gain effects. Such mechanisms are of particular importance for the study of survival/destruction of localised structures in many physical situations. In this work, we prove that in the discrete complex Ginzburg–Landau equation dissipative solitonic waveforms persist for significant times by introducing a dynamical transitivity argument. This argument is based on a combination of the notions of “inviscid limits” and of the “continuous dependence of solutions on their initial data”, between the dissipative system and its Hamiltonian counterparts. Thereby, it establishes closeness of the solutions of the Ginzburg–Landau lattice to those of the conservative ideals described by the Discrete Nonlinear Schrödinger and Ablowitz–Ladik lattices. Such a closeness holds when the initial conditions of the systems are chosen to be sufficiently small in the suitable metrics and for small values of the dissipation or gain strengths. Our numerical findings are in excellent agreement with the analytical predictions for the dynamics of the dissipative bright, dark or even Peregrine-type solitonic waveforms.SpringerFísica Aplicada IFQM280: Física no LinealEU (FEDER program2014-2020) through both Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía under the project P18-RT-3480EU (FEDER program2014-2020) through both Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía under the project US-1380977MCIN/AEI/10.13039/501100011033 under the project PID2019-110430GB-C21MCIN/AEI/10.13039/501100011033 under the project PID2020-112620GB-I002023info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/145357https://doi.org/10.1007/s00332-023-09904-2reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Nonlinear Science, 33 (51).P18-RT-3480US-1380977PID2019-110430GB-C21PID2020-112620GB-I00https://link.springer.com/article/10.1007/s00332-023-09904-2info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1453572026-06-17T12:51:07Z
dc.title.none.fl_str_mv Dissipative Localised Structures for the Complex Discrete Ginzburg–Landau Equation
title Dissipative Localised Structures for the Complex Discrete Ginzburg–Landau Equation
spellingShingle Dissipative Localised Structures for the Complex Discrete Ginzburg–Landau Equation
Hennig, Dirk
Discrete Ginzburg-Landau equation
Ablowitz-Ladik equation
Discrete Nonlinear Schrödinger equations
Dissipative solitons
Persistence
title_short Dissipative Localised Structures for the Complex Discrete Ginzburg–Landau Equation
title_full Dissipative Localised Structures for the Complex Discrete Ginzburg–Landau Equation
title_fullStr Dissipative Localised Structures for the Complex Discrete Ginzburg–Landau Equation
title_full_unstemmed Dissipative Localised Structures for the Complex Discrete Ginzburg–Landau Equation
title_sort Dissipative Localised Structures for the Complex Discrete Ginzburg–Landau Equation
dc.creator.none.fl_str_mv Hennig, Dirk
Karachalios, Nikos I.
Cuevas-Maraver, Jesús
author Hennig, Dirk
author_facet Hennig, Dirk
Karachalios, Nikos I.
Cuevas-Maraver, Jesús
author_role author
author2 Karachalios, Nikos I.
Cuevas-Maraver, Jesús
author2_role author
author
dc.contributor.none.fl_str_mv Física Aplicada I
FQM280: Física no Lineal
EU (FEDER program2014-2020) through both Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía under the project P18-RT-3480
EU (FEDER program2014-2020) through both Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía under the project US-1380977
MCIN/AEI/10.13039/501100011033 under the project PID2019-110430GB-C21
MCIN/AEI/10.13039/501100011033 under the project PID2020-112620GB-I00
dc.subject.none.fl_str_mv Discrete Ginzburg-Landau equation
Ablowitz-Ladik equation
Discrete Nonlinear Schrödinger equations
Dissipative solitons
Persistence
topic Discrete Ginzburg-Landau equation
Ablowitz-Ladik equation
Discrete Nonlinear Schrödinger equations
Dissipative solitons
Persistence
description The discrete complex Ginzburg–Landau equation is a fundamental model for the dynamics of nonlinear lattices incorporating competitive dissipation and energy gain effects. Such mechanisms are of particular importance for the study of survival/destruction of localised structures in many physical situations. In this work, we prove that in the discrete complex Ginzburg–Landau equation dissipative solitonic waveforms persist for significant times by introducing a dynamical transitivity argument. This argument is based on a combination of the notions of “inviscid limits” and of the “continuous dependence of solutions on their initial data”, between the dissipative system and its Hamiltonian counterparts. Thereby, it establishes closeness of the solutions of the Ginzburg–Landau lattice to those of the conservative ideals described by the Discrete Nonlinear Schrödinger and Ablowitz–Ladik lattices. Such a closeness holds when the initial conditions of the systems are chosen to be sufficiently small in the suitable metrics and for small values of the dissipation or gain strengths. Our numerical findings are in excellent agreement with the analytical predictions for the dynamics of the dissipative bright, dark or even Peregrine-type solitonic waveforms.
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/145357
https://doi.org/10.1007/s00332-023-09904-2
url https://hdl.handle.net/11441/145357
https://doi.org/10.1007/s00332-023-09904-2
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Nonlinear Science, 33 (51).
P18-RT-3480
US-1380977
PID2019-110430GB-C21
PID2020-112620GB-I00
https://link.springer.com/article/10.1007/s00332-023-09904-2
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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score 15,301629

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