Solitary waves in a discrete nonlinear Dirac equation

In the present work, we introduce a discrete formulation of the nonlinear Dirac equation in the form of a discretization of the Gross – Neveu model. The motivation for this discrete model proposal is both computational (near the continuum limit) and theoretical (using the understanding of the anti-c...

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Autores: Cuevas-Maraver, Jesús, Kevrekidis, Panayotis G., Saxena, Avadh
Tipo de recurso: artículo
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:11441/24903
Acceso en línea:http://hdl.handle.net/11441/24903
https://doi.org/10.1088/1751-8113/48/5/055204
Access Level:acceso abierto
Palabra clave:solitons
nonlinear Dirac equation
anti-continuum limit
existence
stability
dynamics
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spelling Solitary waves in a discrete nonlinear Dirac equationCuevas-Maraver, JesúsKevrekidis, Panayotis G.Saxena, Avadhsolitonsnonlinear Dirac equationanti-continuum limitexistencestabilitydynamicsIn the present work, we introduce a discrete formulation of the nonlinear Dirac equation in the form of a discretization of the Gross – Neveu model. The motivation for this discrete model proposal is both computational (near the continuum limit) and theoretical (using the understanding of the anti-con- tinuum limit of vanishing coupling). Numerous unexpected features are identi fi ed including a staggered solitary pattern emerging from a single site excitation, as well as two- and three-site excitations playing a role analogous to one- and two-site excitations, respectively, of the discrete nonlinear Schrödinger analogue of the model. Stability exchanges between the two- and three-site states are identi fi ed, as well as instabilities that appear to be per- sistent over the coupling strength ε , for a subcritical value of the propagation constant Λ . Variations of the propagation constant, coupling parameter and nonlinearity exponent are all examined in terms of their existence and stability implications and long dynamical simulations are used to unravel the evolu- tionary phenomenology of the system (when unstable)Física Aplicada I2015info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/24903https://doi.org/10.1088/1751-8113/48/5/055204reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Physics A: Mathematical and Theoretical, 48(5), 055204: 1-22http://iopscience.iop.org/1751-8121/48/5/055204/articledoi:10.1088/1751-8113/48/5/055204info:eu-repo/semantics/openAccessoai:idus.us.es:11441/249032026-06-17T12:51:07Z
dc.title.none.fl_str_mv Solitary waves in a discrete nonlinear Dirac equation
title Solitary waves in a discrete nonlinear Dirac equation
spellingShingle Solitary waves in a discrete nonlinear Dirac equation
Cuevas-Maraver, Jesús
solitons
nonlinear Dirac equation
anti-continuum limit
existence
stability
dynamics
title_short Solitary waves in a discrete nonlinear Dirac equation
title_full Solitary waves in a discrete nonlinear Dirac equation
title_fullStr Solitary waves in a discrete nonlinear Dirac equation
title_full_unstemmed Solitary waves in a discrete nonlinear Dirac equation
title_sort Solitary waves in a discrete nonlinear Dirac equation
dc.creator.none.fl_str_mv Cuevas-Maraver, Jesús
Kevrekidis, Panayotis G.
Saxena, Avadh
author Cuevas-Maraver, Jesús
author_facet Cuevas-Maraver, Jesús
Kevrekidis, Panayotis G.
Saxena, Avadh
author_role author
author2 Kevrekidis, Panayotis G.
Saxena, Avadh
author2_role author
author
dc.contributor.none.fl_str_mv Física Aplicada I
dc.subject.none.fl_str_mv solitons
nonlinear Dirac equation
anti-continuum limit
existence
stability
dynamics
topic solitons
nonlinear Dirac equation
anti-continuum limit
existence
stability
dynamics
description In the present work, we introduce a discrete formulation of the nonlinear Dirac equation in the form of a discretization of the Gross – Neveu model. The motivation for this discrete model proposal is both computational (near the continuum limit) and theoretical (using the understanding of the anti-con- tinuum limit of vanishing coupling). Numerous unexpected features are identi fi ed including a staggered solitary pattern emerging from a single site excitation, as well as two- and three-site excitations playing a role analogous to one- and two-site excitations, respectively, of the discrete nonlinear Schrödinger analogue of the model. Stability exchanges between the two- and three-site states are identi fi ed, as well as instabilities that appear to be per- sistent over the coupling strength ε , for a subcritical value of the propagation constant Λ . Variations of the propagation constant, coupling parameter and nonlinearity exponent are all examined in terms of their existence and stability implications and long dynamical simulations are used to unravel the evolu- tionary phenomenology of the system (when unstable)
publishDate 2015
dc.date.none.fl_str_mv 2015
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/24903
https://doi.org/10.1088/1751-8113/48/5/055204
url http://hdl.handle.net/11441/24903
https://doi.org/10.1088/1751-8113/48/5/055204
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Physics A: Mathematical and Theoretical, 48(5), 055204: 1-22
http://iopscience.iop.org/1751-8121/48/5/055204/article
doi:10.1088/1751-8113/48/5/055204
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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