Discrete derivative nonlinear Schrödinger equations

We consider novel discrete derivative nonlinear Schrödinger equations (ddNLSs). Taking the continuum derivative nonlinear Schrödinger equation (dNLS), we use for the discretisation of the derivative the forward, backward, and central difference schemes, respectively, and term the corresponding equat...

ver descrição completa

Detalhes bibliográficos
Autores: Hennig, Dirk, Cuevas-Maraver, Jesús
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:11441/168303
Acesso em linha:https://hdl.handle.net/11441/168303
https://doi.org/10.3390/math13010105
Access Level:acceso abierto
Palavra-chave:Discrete derivative nonlinear Schrödinger equations
Solitons
Asymptotic behaviour of solutions
Travelling solitary waves
id ES_662a06e1066f228c2d4d2f10b2e9bfd0
oai_identifier_str oai:idus.us.es:11441/168303
network_acronym_str ES
network_name_str España
repository_id_str
spelling Discrete derivative nonlinear Schrödinger equationsHennig, DirkCuevas-Maraver, JesúsDiscrete derivative nonlinear Schrödinger equationsSolitonsAsymptotic behaviour of solutionsTravelling solitary wavesWe consider novel discrete derivative nonlinear Schrödinger equations (ddNLSs). Taking the continuum derivative nonlinear Schrödinger equation (dNLS), we use for the discretisation of the derivative the forward, backward, and central difference schemes, respectively, and term the corresponding equations forward, backward, and central ddNLSs. We show that in contrast to the dNLS, which is completely integrable and supports soliton solutions, the forward and backward ddNLSs can be either dissipative or expansive. As a consequence, solutions of the forward and backward ddNLSs behave drastically differently compared to those of the (integrable) dNLS. For the dissipative forward ddNLS, all solutions decay asymptotically to zero, whereas for the expansive forward ddNLS all solutions grow exponentially in time, features that are not present in the dynamics of the (integrable) dNLS. In comparison, the central ddNLS is characterized by conservative dynamics. Remarkably, for the central ddNLS the total momentum is conserved, allowing the existence of solitary travelling wave (TW) solutions. In fact, we prove the existence of solitary TWs, facilitating Schauder’s fixed-point theorem. For the damped forward expansive ddNLS we demonstrate that there exists such a balance of dissipation so that solitary stationary modes exist.MDPIFísica Aplicada IFQM280: Física no Lineal2024info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/168303https://doi.org/10.3390/math13010105reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésMathematics, 13 (1), 105.MCIN/AEI/10.13039/501100011033PID2020-112620GB-I00PID2022-143120OB-I00https://www.mdpi.com/2227-7390/13/1/105info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1683032026-06-17T12:51:07Z
dc.title.none.fl_str_mv Discrete derivative nonlinear Schrödinger equations
title Discrete derivative nonlinear Schrödinger equations
spellingShingle Discrete derivative nonlinear Schrödinger equations
Hennig, Dirk
Discrete derivative nonlinear Schrödinger equations
Solitons
Asymptotic behaviour of solutions
Travelling solitary waves
title_short Discrete derivative nonlinear Schrödinger equations
title_full Discrete derivative nonlinear Schrödinger equations
title_fullStr Discrete derivative nonlinear Schrödinger equations
title_full_unstemmed Discrete derivative nonlinear Schrödinger equations
title_sort Discrete derivative nonlinear Schrödinger equations
dc.creator.none.fl_str_mv Hennig, Dirk
Cuevas-Maraver, Jesús
author Hennig, Dirk
author_facet Hennig, Dirk
Cuevas-Maraver, Jesús
author_role author
author2 Cuevas-Maraver, Jesús
author2_role author
dc.contributor.none.fl_str_mv Física Aplicada I
FQM280: Física no Lineal
dc.subject.none.fl_str_mv Discrete derivative nonlinear Schrödinger equations
Solitons
Asymptotic behaviour of solutions
Travelling solitary waves
topic Discrete derivative nonlinear Schrödinger equations
Solitons
Asymptotic behaviour of solutions
Travelling solitary waves
description We consider novel discrete derivative nonlinear Schrödinger equations (ddNLSs). Taking the continuum derivative nonlinear Schrödinger equation (dNLS), we use for the discretisation of the derivative the forward, backward, and central difference schemes, respectively, and term the corresponding equations forward, backward, and central ddNLSs. We show that in contrast to the dNLS, which is completely integrable and supports soliton solutions, the forward and backward ddNLSs can be either dissipative or expansive. As a consequence, solutions of the forward and backward ddNLSs behave drastically differently compared to those of the (integrable) dNLS. For the dissipative forward ddNLS, all solutions decay asymptotically to zero, whereas for the expansive forward ddNLS all solutions grow exponentially in time, features that are not present in the dynamics of the (integrable) dNLS. In comparison, the central ddNLS is characterized by conservative dynamics. Remarkably, for the central ddNLS the total momentum is conserved, allowing the existence of solitary travelling wave (TW) solutions. In fact, we prove the existence of solitary TWs, facilitating Schauder’s fixed-point theorem. For the damped forward expansive ddNLS we demonstrate that there exists such a balance of dissipation so that solitary stationary modes exist.
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/11441/168303
https://doi.org/10.3390/math13010105
url https://hdl.handle.net/11441/168303
https://doi.org/10.3390/math13010105
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Mathematics, 13 (1), 105.
MCIN/AEI/10.13039/501100011033
PID2020-112620GB-I00
PID2022-143120OB-I00
https://www.mdpi.com/2227-7390/13/1/105
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
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869409795852730368
score 15,812455

Registos relacionados