Extended Symmetry of Higher Painlevé Equations of Even Periodicity and Their Rational Solutions

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MetadadosDescriçãoIdioma
Autor(es): dc.contributorUniversity of Illinois at Chicago-
Autor(es): dc.contributorUniversidade Estadual Paulista (UNESP)-
Autor(es): dc.creatorAratyn, Henrik-
Autor(es): dc.creatorGomes, José Francisco-
Autor(es): dc.creatorLobo, Gabriel Vieira-
Autor(es): dc.creatorZimerman, Abraham Hirsz-
Data de aceite: dc.date.accessioned2025-08-21T16:53:03Z-
Data de disponibilização: dc.date.available2025-08-21T16:53:03Z-
Data de envio: dc.date.issued2025-04-29-
Data de envio: dc.date.issued2024-11-30-
Fonte completa do material: dc.identifierhttp://dx.doi.org/10.3390/math12233701-
Fonte completa do material: dc.identifierhttps://hdl.handle.net/11449/304234-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/11449/304234-
Descrição: dc.descriptionThe structure of the extended affine Weyl symmetry group of higher Painlevé equations of N periodicity depends on whether N is even or odd. We find that for even N, the symmetry group (Formula presented.) contains the conventional Bäcklund transformations (Formula presented.), the group of automorphisms consisting of cycling permutations but also reflections on a periodic circle of N points, which is a novel feature uncovered in this paper. The presence of reflection automorphisms is connected to the existence of degenerated solutions, and for (Formula presented.), we explicitly show how even reflection automorphisms cause degeneracy of a class of rational solutions obtained on the orbit of the translation operators of (Formula presented.). We obtain the closed expressions for the solutions and their degenerated counterparts in terms of the determinants of the Kummer polynomials.-
Descrição: dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)-
Descrição: dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)-
Descrição: dc.descriptionDepartment of Physics University of Illinois at Chicago, 845 W. Taylor Str.-
Descrição: dc.descriptionInstituto de Física Teórica-UNESP, Rua Dr Bento Teobaldo Ferraz 271, Bloco II, São Paulo-
Descrição: dc.descriptionInstituto de Física Teórica-UNESP, Rua Dr Bento Teobaldo Ferraz 271, Bloco II, São Paulo-
Idioma: dc.languageen-
Relação: dc.relationMathematics-
???dc.source???: dc.sourceScopus-
Palavras-chave: dc.subjectaffine Weyl symmetries-
Palavras-chave: dc.subjectBäcklund transformations-
Palavras-chave: dc.subjectdressing chain equations-
Palavras-chave: dc.subjectKummer polynomials-
Palavras-chave: dc.subjectPainlevé equations-
Título: dc.titleExtended Symmetry of Higher Painlevé Equations of Even Periodicity and Their Rational Solutions-
Tipo de arquivo: dc.typelivro digital-
Aparece nas coleções:Repositório Institucional - Unesp

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