Generalized Bäcklund transformations for affine Toda 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/abd8b2
http://hdl.handle.net/11449/207275
Resumo: The construction of generalized Bäcklund transformation for the An affine Toda hierarchy is proposed in terms of gauge transformation acting on the zero curvature representation. Such construction is based upon the graded structure of the underlying affine algebra which induces a classification of generalized Bäcklund transformations. Moreover, explicit examples for sl(3) and sl(4) lead to uncover interesting composition properties of various types of Bäcklund transformations. The universality character of the gauge-Bäcklund transformation method is extended to all equations of the hierarchy. Such interesting property provides a systematic framework to construct Bäcklund transformations to higher flow equations. Explicit example for the simplest higher flow of the sl(3) hierarchy is presented.
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spelling Generalized Bäcklund transformations for affine Toda hierarchiesBacklund transformationIntegrable hierarchiesSolitonsThe construction of generalized Bäcklund transformation for the An affine Toda hierarchy is proposed in terms of gauge transformation acting on the zero curvature representation. Such construction is based upon the graded structure of the underlying affine algebra which induces a classification of generalized Bäcklund transformations. Moreover, explicit examples for sl(3) and sl(4) lead to uncover interesting composition properties of various types of Bäcklund transformations. The universality character of the gauge-Bäcklund transformation method is extended to all equations of the hierarchy. Such interesting property provides a systematic framework to construct Bäcklund transformations to higher flow equations. Explicit example for the simplest higher flow of the sl(3) hierarchy is presented.Instituto de Física Téorica - IFT/UNESP, Rua Dr. Bento Teobaldo Ferraz, 271, Bloco IIInstituto de Física Téorica - 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]2021-06-25T10:52:19Z2021-06-25T10:52:19Z2021-02-12info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1088/1751-8121/abd8b2Journal of Physics A: Mathematical and Theoretical, v. 54, n. 6, 2021.1751-81211751-8113http://hdl.handle.net/11449/20727510.1088/1751-8121/abd8b22-s2.0-85100798716Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Physics A: Mathematical and Theoreticalinfo:eu-repo/semantics/openAccess2021-10-23T16:43:33Zoai:repositorio.unesp.br:11449/207275Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T23:51:03.971106Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Generalized Bäcklund transformations for affine Toda hierarchies
title Generalized Bäcklund transformations for affine Toda hierarchies
spellingShingle Generalized Bäcklund transformations for affine Toda hierarchies
De Carvalho Ferreira, J. M. [UNESP]
Backlund transformation
Integrable hierarchies
Solitons
title_short Generalized Bäcklund transformations for affine Toda hierarchies
title_full Generalized Bäcklund transformations for affine Toda hierarchies
title_fullStr Generalized Bäcklund transformations for affine Toda hierarchies
title_full_unstemmed Generalized Bäcklund transformations for affine Toda hierarchies
title_sort Generalized Bäcklund transformations for affine Toda 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
Solitons
topic Backlund transformation
Integrable hierarchies
Solitons
description The construction of generalized Bäcklund transformation for the An affine Toda hierarchy is proposed in terms of gauge transformation acting on the zero curvature representation. Such construction is based upon the graded structure of the underlying affine algebra which induces a classification of generalized Bäcklund transformations. Moreover, explicit examples for sl(3) and sl(4) lead to uncover interesting composition properties of various types of Bäcklund transformations. The universality character of the gauge-Bäcklund transformation method is extended to all equations of the hierarchy. Such interesting property provides a systematic framework to construct Bäcklund transformations to higher flow equations. Explicit example for the simplest higher flow of the sl(3) hierarchy is presented.
publishDate 2021
dc.date.none.fl_str_mv 2021-06-25T10:52:19Z
2021-06-25T10:52:19Z
2021-02-12
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/abd8b2
Journal of Physics A: Mathematical and Theoretical, v. 54, n. 6, 2021.
1751-8121
1751-8113
http://hdl.handle.net/11449/207275
10.1088/1751-8121/abd8b2
2-s2.0-85100798716
url http://dx.doi.org/10.1088/1751-8121/abd8b2
http://hdl.handle.net/11449/207275
identifier_str_mv Journal of Physics A: Mathematical and Theoretical, v. 54, n. 6, 2021.
1751-8121
1751-8113
10.1088/1751-8121/abd8b2
2-s2.0-85100798716
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
_version_ 1808129558659989504

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