The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: Scalar and matrix cases

We are grateful to the Ministry of Economy and Competitiveness of Spain for funding under grant number MTM2016-80276-P (AEI/FEDER, EU).

Detalles Bibliográficos
Autores: Pickering, Andrew, Gordoa, Pilar R, Wattis, Jonathan A D
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universidad Rey Juan Carlos
Repositorio:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
OAI Identifier:oai:burjcdigital.urjc.es:10115/42249
Acceso en línea:https://hdl.handle.net/10115/42249
Access Level:acceso abierto
Palabra clave:matrix semidiscrete equations
asymptotic behaviour
Hamiltonian formulations of matrix Painlevé equations
solutions of matrix second Painlevé equation
integrable systems
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spelling The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: Scalar and matrix casesPickering, AndrewGordoa, Pilar RWattis, Jonathan A Dmatrix semidiscrete equationsasymptotic behaviourHamiltonian formulations of matrix Painlevé equationssolutions of matrix second Painlevé equationintegrable systemsWe are grateful to the Ministry of Economy and Competitiveness of Spain for funding under grant number MTM2016-80276-P (AEI/FEDER, EU).In this paper we consider the matrix nonautonomous semidiscrete (or lattice) equation U_{n,t} = (2n − 1)(U_{n+1} − U_{n−1})^{-1}, as well as the scalar case thereof. This equation was recently derived in the context of auto-Bäcklund transformations for a matrix partial differential equation. We use asymptotic techniques to reveal a connection between this equation and the matrix (or, as appropriate, scalar) first Painlevé equation. In the matrix case, we also discuss our asymptotic analysis more generally, as well as considering a component-wise approach. In addition, Hamiltonian formulations of the matrix first and second Painlevé equations are given, as well as a discussion of classes of solutions of the matrix second Painlevé equation.Elsevier202420242019info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10115/42249reponame:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlosinstname:Universidad Rey Juan CarlosInglésAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:burjcdigital.urjc.es:10115/422492026-06-24T12:48:17Z
dc.title.none.fl_str_mv The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: Scalar and matrix cases
title The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: Scalar and matrix cases
spellingShingle The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: Scalar and matrix cases
Pickering, Andrew
matrix semidiscrete equations
asymptotic behaviour
Hamiltonian formulations of matrix Painlevé equations
solutions of matrix second Painlevé equation
integrable systems
title_short The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: Scalar and matrix cases
title_full The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: Scalar and matrix cases
title_fullStr The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: Scalar and matrix cases
title_full_unstemmed The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: Scalar and matrix cases
title_sort The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: Scalar and matrix cases
dc.creator.none.fl_str_mv Pickering, Andrew
Gordoa, Pilar R
Wattis, Jonathan A D
author Pickering, Andrew
author_facet Pickering, Andrew
Gordoa, Pilar R
Wattis, Jonathan A D
author_role author
author2 Gordoa, Pilar R
Wattis, Jonathan A D
author2_role author
author
dc.subject.none.fl_str_mv matrix semidiscrete equations
asymptotic behaviour
Hamiltonian formulations of matrix Painlevé equations
solutions of matrix second Painlevé equation
integrable systems
topic matrix semidiscrete equations
asymptotic behaviour
Hamiltonian formulations of matrix Painlevé equations
solutions of matrix second Painlevé equation
integrable systems
description We are grateful to the Ministry of Economy and Competitiveness of Spain for funding under grant number MTM2016-80276-P (AEI/FEDER, EU).
publishDate 2019
dc.date.none.fl_str_mv 2019
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10115/42249
url https://hdl.handle.net/10115/42249
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
instname:Universidad Rey Juan Carlos
instname_str Universidad Rey Juan Carlos
reponame_str BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
collection BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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