Gauge Miura and Bäcklund transformations for generalized An-KdV hierarchies

Detalhes bibliográficos
Autor(a) principal: De Carvalho Ferreira, J. M. [UNESP]
Data de Publicação: 2021
Outros Autores: Gomes, J. F. [UNESP], Lobo, G. V. [UNESP], Zimerman, A. H. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1088/1751-8121/ac2718
http://hdl.handle.net/11449/229661
Resumo: The construction of Miura and Bäcklund transformations for An mKdV and KdV hierarchies are presented in terms of gauge transformations acting upon the zero curvature representation. As in thewell knownsl(2) case, we derive and relate the equations of motion for the two hierarchies. Moreover, the Miuragauge transformation is not unique, instead, it is shown to be connected to a set of generators labeled by the exponents of An. The construction of generalized gauge-Bäcklund transformation for the An-KdV hierarchy is obtained as a composition ofMiura and Bäcklund-gauge transformations for An-mKdV hierarchy. The zero curvature representation provide a framework which is universal within all flows and generate systematically Bäcklund transformations for the entirely hierarchy.
id UNSP_b476de997c1214ca7d0f70d2b6471b42
oai_identifier_str oai:repositorio.unesp.br:11449/229661
network_acronym_str UNSP
network_name_str Repositório Institucional da UNESP
repository_id_str 2946
spelling Gauge Miura and Bäcklund transformations for generalized An-KdV hierarchiesBacklund transformationIntegrable hierarchiesMiura transformationSolitonsThe construction of Miura and Bäcklund transformations for An mKdV and KdV hierarchies are presented in terms of gauge transformations acting upon the zero curvature representation. As in thewell knownsl(2) case, we derive and relate the equations of motion for the two hierarchies. Moreover, the Miuragauge transformation is not unique, instead, it is shown to be connected to a set of generators labeled by the exponents of An. The construction of generalized gauge-Bäcklund transformation for the An-KdV hierarchy is obtained as a composition ofMiura and Bäcklund-gauge transformations for An-mKdV hierarchy. The zero curvature representation provide a framework which is universal within all flows and generate systematically Bäcklund transformations for the entirely hierarchy.Instituto de Física Teórica-IFT/UNESP, Rua Dr. Bento Teobaldo Ferraz 271., Bloco IIInstituto de Física Teórica-IFT/UNESP, Rua Dr. Bento Teobaldo Ferraz 271., Bloco IIUniversidade Estadual Paulista (UNESP)De Carvalho Ferreira, J. M. [UNESP]Gomes, J. F. [UNESP]Lobo, G. V. [UNESP]Zimerman, A. H. [UNESP]2022-04-29T08:35:00Z2022-04-29T08:35:00Z2021-10-29info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1088/1751-8121/ac2718Journal of Physics A: Mathematical and Theoretical, v. 54, n. 43, 2021.1751-81211751-8113http://hdl.handle.net/11449/22966110.1088/1751-8121/ac27182-s2.0-85116533512Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Physics A: Mathematical and Theoreticalinfo:eu-repo/semantics/openAccess2024-11-25T14:27:43Zoai:repositorio.unesp.br:11449/229661Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462024-11-25T14:27:43Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Gauge Miura and Bäcklund transformations for generalized An-KdV hierarchies
title Gauge Miura and Bäcklund transformations for generalized An-KdV hierarchies
spellingShingle Gauge Miura and Bäcklund transformations for generalized An-KdV hierarchies
De Carvalho Ferreira, J. M. [UNESP]
Backlund transformation
Integrable hierarchies
Miura transformation
Solitons
title_short Gauge Miura and Bäcklund transformations for generalized An-KdV hierarchies
title_full Gauge Miura and Bäcklund transformations for generalized An-KdV hierarchies
title_fullStr Gauge Miura and Bäcklund transformations for generalized An-KdV hierarchies
title_full_unstemmed Gauge Miura and Bäcklund transformations for generalized An-KdV hierarchies
title_sort Gauge Miura and Bäcklund transformations for generalized An-KdV hierarchies
author De Carvalho Ferreira, J. M. [UNESP]
author_facet De Carvalho Ferreira, J. M. [UNESP]
Gomes, J. F. [UNESP]
Lobo, G. V. [UNESP]
Zimerman, A. H. [UNESP]
author_role author
author2 Gomes, J. F. [UNESP]
Lobo, G. V. [UNESP]
Zimerman, A. H. [UNESP]
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv De Carvalho Ferreira, J. M. [UNESP]
Gomes, J. F. [UNESP]
Lobo, G. V. [UNESP]
Zimerman, A. H. [UNESP]
dc.subject.por.fl_str_mv Backlund transformation
Integrable hierarchies
Miura transformation
Solitons
topic Backlund transformation
Integrable hierarchies
Miura transformation
Solitons
description The construction of Miura and Bäcklund transformations for An mKdV and KdV hierarchies are presented in terms of gauge transformations acting upon the zero curvature representation. As in thewell knownsl(2) case, we derive and relate the equations of motion for the two hierarchies. Moreover, the Miuragauge transformation is not unique, instead, it is shown to be connected to a set of generators labeled by the exponents of An. The construction of generalized gauge-Bäcklund transformation for the An-KdV hierarchy is obtained as a composition ofMiura and Bäcklund-gauge transformations for An-mKdV hierarchy. The zero curvature representation provide a framework which is universal within all flows and generate systematically Bäcklund transformations for the entirely hierarchy.
publishDate 2021
dc.date.none.fl_str_mv 2021-10-29
2022-04-29T08:35:00Z
2022-04-29T08:35:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1088/1751-8121/ac2718
Journal of Physics A: Mathematical and Theoretical, v. 54, n. 43, 2021.
1751-8121
1751-8113
http://hdl.handle.net/11449/229661
10.1088/1751-8121/ac2718
2-s2.0-85116533512
url http://dx.doi.org/10.1088/1751-8121/ac2718
http://hdl.handle.net/11449/229661
identifier_str_mv Journal of Physics A: Mathematical and Theoretical, v. 54, n. 43, 2021.
1751-8121
1751-8113
10.1088/1751-8121/ac2718
2-s2.0-85116533512
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal of Physics A: Mathematical and Theoretical
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv repositoriounesp@unesp.br
_version_ 1826304244298285056

Registros relacionados