Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-24T10:06:11.985Z Has data issue: false hasContentIssue false
  • English
  • Français

Truncation-type methods and Bäcklund transformations for ordinary differential equations: the third and fifth Painlevé equations

Published online by Cambridge University Press:  19 July 2002

P. R. Gordoa ,
N. Joshi  and
A. Pickering
P. R. Gordoa
Affiliation:
Area de Fisica Teórica, Facultad de Ciencias, Edificio de Fisica, Universidad de Salamanca, 37008 Salamanca, Spain e-mail: prg@sonia.usal.es e-mail: andrew@sonia.usal.es
N. Joshi
Affiliation:
Department of Pure Mathematics, University of Adelaide, Adelaide, Australia 5005 e-mail: nalini.joshi@adelaide.edu.au
A. Pickering
Affiliation:
Area de Fisica Teórica, Facultad de Ciencias, Edificio de Fisica, Universidad de Salamanca, 37008 Salamanca, Spain e-mail: prg@sonia.usal.es e-mail: andrew@sonia.usal.es
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In a recent paper we presented a truncation-type method of deriving Bäcklund transformations for ordinary differential equations. This method is based on a consideration of truncation as a mapping that preserves the locations of a natural subset of the movable poles that the equation possesses. Here we apply this approach to the third and fifth Painlevé equations. For the third Painlevé equation we are able to obtain all fundamental Bäcklund transformations for the case where the parameters satisfy \gamma \delta \neq 0. For the fifth Painlevé equation our approach yields what appears to be all known Bäcklund transformations.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 43 , Issue A , June 2001 , pp. 23 - 32
Copyright
© 2001 Glasgow Mathematical Journal Trust