Twisted Affine Integrable Hierarchies and Soliton Solutions

Detalhes bibliográficos
Autor(a) principal: Adans, Y. F. [UNESP]
Data de Publicação: 2023
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/10.1007/s13538-022-01230-4
http://hdl.handle.net/11449/248039
Resumo: A systematic construction of a class of integrable hierarchy is discussed in terms of the twisted affine A2r(2) Lie algebra. The zero curvature representation of the time evolution equations is shown to be classified according to its algebraic structure and according to its vacuum solutions. It is shown that a class of models admit both zero and constant (non-zero) vacuum solutions. Another consists essentially of integral non-local equations and can be classified into two sub-classes, one admitting only zero vacuum and another of constant strictly non-zero vacuum solutions. The two-dimensional gauge potentials in the vacuum play a crucial ingredient and are shown to be expanded in powers of the vacuum parameter v. Soliton solutions are constructed from vertex operators, which for the non-zero vacuum solutions correspond to deformations characterized by v.
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spelling Twisted Affine Integrable Hierarchies and Soliton SolutionsIntegrable hierarchiesKac-Moody algebrasSoliton solutionsVertex operatorsA systematic construction of a class of integrable hierarchy is discussed in terms of the twisted affine A2r(2) Lie algebra. The zero curvature representation of the time evolution equations is shown to be classified according to its algebraic structure and according to its vacuum solutions. It is shown that a class of models admit both zero and constant (non-zero) vacuum solutions. Another consists essentially of integral non-local equations and can be classified into two sub-classes, one admitting only zero vacuum and another of constant strictly non-zero vacuum solutions. The two-dimensional gauge potentials in the vacuum play a crucial ingredient and are shown to be expanded in powers of the vacuum parameter v. Soliton solutions are constructed from vertex operators, which for the non-zero vacuum solutions correspond to deformations characterized by v.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Instituto de Física Teórica - IFT/UNESP, Rua Dr. Bento Teobaldo Ferraz, 271, Bloco II, SPInstituto de Física Teórica - IFT/UNESP, Rua Dr. Bento Teobaldo Ferraz, 271, Bloco II, SPFAPESP: 2021/00623-4Universidade Estadual Paulista (UNESP)Adans, Y. F. [UNESP]Gomes, J. F. [UNESP]Lobo, G. V. [UNESP]Zimerman, A. H. [UNESP]2023-07-29T13:32:50Z2023-07-29T13:32:50Z2023-02-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1007/s13538-022-01230-4Brazilian Journal of Physics, v. 53, n. 1, 2023.1678-44480103-9733http://hdl.handle.net/11449/24803910.1007/s13538-022-01230-42-s2.0-85144095751Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengBrazilian Journal of Physicsinfo:eu-repo/semantics/openAccess2023-07-29T13:32:50Zoai:repositorio.unesp.br:11449/248039Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T17:02:13.837518Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Twisted Affine Integrable Hierarchies and Soliton Solutions
title Twisted Affine Integrable Hierarchies and Soliton Solutions
spellingShingle Twisted Affine Integrable Hierarchies and Soliton Solutions
Adans, Y. F. [UNESP]
Integrable hierarchies
Kac-Moody algebras
Soliton solutions
Vertex operators
title_short Twisted Affine Integrable Hierarchies and Soliton Solutions
title_full Twisted Affine Integrable Hierarchies and Soliton Solutions
title_fullStr Twisted Affine Integrable Hierarchies and Soliton Solutions
title_full_unstemmed Twisted Affine Integrable Hierarchies and Soliton Solutions
title_sort Twisted Affine Integrable Hierarchies and Soliton Solutions
author Adans, Y. F. [UNESP]
author_facet Adans, Y. F. [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 Adans, Y. F. [UNESP]
Gomes, J. F. [UNESP]
Lobo, G. V. [UNESP]
Zimerman, A. H. [UNESP]
dc.subject.por.fl_str_mv Integrable hierarchies
Kac-Moody algebras
Soliton solutions
Vertex operators
topic Integrable hierarchies
Kac-Moody algebras
Soliton solutions
Vertex operators
description A systematic construction of a class of integrable hierarchy is discussed in terms of the twisted affine A2r(2) Lie algebra. The zero curvature representation of the time evolution equations is shown to be classified according to its algebraic structure and according to its vacuum solutions. It is shown that a class of models admit both zero and constant (non-zero) vacuum solutions. Another consists essentially of integral non-local equations and can be classified into two sub-classes, one admitting only zero vacuum and another of constant strictly non-zero vacuum solutions. The two-dimensional gauge potentials in the vacuum play a crucial ingredient and are shown to be expanded in powers of the vacuum parameter v. Soliton solutions are constructed from vertex operators, which for the non-zero vacuum solutions correspond to deformations characterized by v.
publishDate 2023
dc.date.none.fl_str_mv 2023-07-29T13:32:50Z
2023-07-29T13:32:50Z
2023-02-01
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/10.1007/s13538-022-01230-4
Brazilian Journal of Physics, v. 53, n. 1, 2023.
1678-4448
0103-9733
http://hdl.handle.net/11449/248039
10.1007/s13538-022-01230-4
2-s2.0-85144095751
url http://dx.doi.org/10.1007/s13538-022-01230-4
http://hdl.handle.net/11449/248039
identifier_str_mv Brazilian Journal of Physics, v. 53, n. 1, 2023.
1678-4448
0103-9733
10.1007/s13538-022-01230-4
2-s2.0-85144095751
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Brazilian Journal of Physics
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
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