On Rational Solutions of Dressing Chains of Even Periodicity

Detalhes bibliográficos
Autor(a) principal: Aratyn, Henrik
Data de Publicação: 2023
Outros Autores: Gomes, José Francisco [UNESP], Lobo, Gabriel Vieira [UNESP], Zimerman, Abraham Hirsz [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.3390/sym15010249
http://hdl.handle.net/11449/248255
Resumo: We develop a systematic approach to deriving rational solutions and obtaining classification of their parameters for dressing chains of even N periodicity or equivalent Painlevé equations invariant under (Formula presented.) symmetry. This formalism identifies rational solutions (as well as special function solutions) with points on orbits of fundamental shift operators of (Formula presented.) affine Weyl groups acting on seed configurations defined as first-order polynomial solutions of the underlying dressing chains. This approach clarifies the structure of rational solutions and establishes an explicit and systematic method towards their construction. For the special case of the (Formula presented.) dressing chain equations, the method yields all the known rational (and special function) solutions of the Painlevé V equation. The formalism naturally extends to (Formula presented.) and beyond as shown in the paper.
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spelling On Rational Solutions of Dressing Chains of Even Periodicityaffine Weyl symmetriesBäcklund transformationsdressing chain equationsHamilton equationsPainlevé equationsWe develop a systematic approach to deriving rational solutions and obtaining classification of their parameters for dressing chains of even N periodicity or equivalent Painlevé equations invariant under (Formula presented.) symmetry. This formalism identifies rational solutions (as well as special function solutions) with points on orbits of fundamental shift operators of (Formula presented.) affine Weyl groups acting on seed configurations defined as first-order polynomial solutions of the underlying dressing chains. This approach clarifies the structure of rational solutions and establishes an explicit and systematic method towards their construction. For the special case of the (Formula presented.) dressing chain equations, the method yields all the known rational (and special function) solutions of the Painlevé V equation. The formalism naturally extends to (Formula presented.) and beyond as shown in the paper.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Department of Physics University of Illinois at Chicago, 845 W. Taylor St.Instituto de Física Teórica-UNESP, Rua Dr Bento Teobaldo Ferraz 271, Bloco IIInstituto de Física Teórica-UNESP, Rua Dr Bento Teobaldo Ferraz 271, Bloco IIUniversity of Illinois at ChicagoUniversidade Estadual Paulista (UNESP)Aratyn, HenrikGomes, José Francisco [UNESP]Lobo, Gabriel Vieira [UNESP]Zimerman, Abraham Hirsz [UNESP]2023-07-29T13:38:52Z2023-07-29T13:38:52Z2023-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.3390/sym15010249Symmetry, v. 15, n. 1, 2023.2073-8994http://hdl.handle.net/11449/24825510.3390/sym150102492-s2.0-85146763895Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengSymmetryinfo:eu-repo/semantics/openAccess2023-07-29T13:38:52Zoai:repositorio.unesp.br:11449/248255Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T22:43:48.521287Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv On Rational Solutions of Dressing Chains of Even Periodicity
title On Rational Solutions of Dressing Chains of Even Periodicity
spellingShingle On Rational Solutions of Dressing Chains of Even Periodicity
Aratyn, Henrik
affine Weyl symmetries
Bäcklund transformations
dressing chain equations
Hamilton equations
Painlevé equations
title_short On Rational Solutions of Dressing Chains of Even Periodicity
title_full On Rational Solutions of Dressing Chains of Even Periodicity
title_fullStr On Rational Solutions of Dressing Chains of Even Periodicity
title_full_unstemmed On Rational Solutions of Dressing Chains of Even Periodicity
title_sort On Rational Solutions of Dressing Chains of Even Periodicity
author Aratyn, Henrik
author_facet Aratyn, Henrik
Gomes, José Francisco [UNESP]
Lobo, Gabriel Vieira [UNESP]
Zimerman, Abraham Hirsz [UNESP]
author_role author
author2 Gomes, José Francisco [UNESP]
Lobo, Gabriel Vieira [UNESP]
Zimerman, Abraham Hirsz [UNESP]
author2_role author
author
author
dc.contributor.none.fl_str_mv University of Illinois at Chicago
Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Aratyn, Henrik
Gomes, José Francisco [UNESP]
Lobo, Gabriel Vieira [UNESP]
Zimerman, Abraham Hirsz [UNESP]
dc.subject.por.fl_str_mv affine Weyl symmetries
Bäcklund transformations
dressing chain equations
Hamilton equations
Painlevé equations
topic affine Weyl symmetries
Bäcklund transformations
dressing chain equations
Hamilton equations
Painlevé equations
description We develop a systematic approach to deriving rational solutions and obtaining classification of their parameters for dressing chains of even N periodicity or equivalent Painlevé equations invariant under (Formula presented.) symmetry. This formalism identifies rational solutions (as well as special function solutions) with points on orbits of fundamental shift operators of (Formula presented.) affine Weyl groups acting on seed configurations defined as first-order polynomial solutions of the underlying dressing chains. This approach clarifies the structure of rational solutions and establishes an explicit and systematic method towards their construction. For the special case of the (Formula presented.) dressing chain equations, the method yields all the known rational (and special function) solutions of the Painlevé V equation. The formalism naturally extends to (Formula presented.) and beyond as shown in the paper.
publishDate 2023
dc.date.none.fl_str_mv 2023-07-29T13:38:52Z
2023-07-29T13:38:52Z
2023-01-01
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/10.3390/sym15010249
Symmetry, v. 15, n. 1, 2023.
2073-8994
http://hdl.handle.net/11449/248255
10.3390/sym15010249
2-s2.0-85146763895
url http://dx.doi.org/10.3390/sym15010249
http://hdl.handle.net/11449/248255
identifier_str_mv Symmetry, v. 15, n. 1, 2023.
2073-8994
10.3390/sym15010249
2-s2.0-85146763895
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Symmetry
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_ 1808129455462285313

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