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

dc.contributor.authorPickering, Andrew
dc.contributor.authorGordoa, Pilar R
dc.contributor.authorWattis, Jonathan A D
dc.date.accessioned2024-12-02T14:19:55Z
dc.date.available2024-12-02T14:19:55Z
dc.date.issued2019
dc.descriptionWe are grateful to the Ministry of Economy and Competitiveness of Spain for funding under grant number MTM2016-80276-P (AEI/FEDER, EU).es
dc.description.abstractIn 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.es
dc.identifier.citationPhysica D 391 (2019) 72–86es
dc.identifier.citationAndrew Pickering, Pilar R. Gordoa, Jonathan A.D. Wattis, The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: Scalar and matrix cases, Physica D: Nonlinear Phenomena, Volume 391, 2019, Pages 72-86, ISSN 0167-2789, https://doi.org/10.1016/j.physd.2018.12.001
dc.identifier.doi10.1016/j.physd.2018.12.001es
dc.identifier.issn0167-2789
dc.identifier.urihttps://hdl.handle.net/10115/42249
dc.language.isoenges
dc.publisherElsevieres
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectmatrix semidiscrete equationses
dc.subjectasymptotic behavioures
dc.subjectHamiltonian formulations of matrix Painlevé equationses
dc.subjectsolutions of matrix second Painlevé equationes
dc.subjectintegrable systemses
dc.titleThe second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: Scalar and matrix caseses
dc.typeinfo:eu-repo/semantics/articlees

Archivos

Bloque original

Mostrando 1 - 1 de 1
Cargando...
Miniatura
Nombre:
2019_Physica_D.pdf
Tamaño:
344.38 KB
Formato:
Adobe Portable Document Format
Descripción:

Bloque de licencias

Mostrando 1 - 1 de 1
No hay miniatura disponible
Nombre:
license.txt
Tamaño:
2.67 KB
Formato:
Item-specific license agreed upon to submission
Descripción: