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Type: Journal article
Title: Truncation-type methods and Bäcklund transformations for ordinary differential equations: The third and fifth Painlevé equations
Other Titles: Truncation-type methods and Backlund transformations for ordinary differential equations: The third and fifth Painleve equations
Author: Gordoa, Pilar
Joshi, Nalini
Pickering, Andrew
Citation: Glasgow Mathematical Journal, 2001; 43(A):23-32
Publisher: Cambridge University Press
Issue Date: 2001
ISSN: 0017-0895
School/Discipline: School of Mathematical Sciences
Statement of
P. R. Gordoa, N. Joshi and A. Pickering
Abstract: 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.
Description: Additional volume of selected papers from a Conference on Integrable Systems, Islay 1999
Provenance: Published online by Cambridge University Press 19 Jul 2002
Rights: © Glasgow Mathematical Journal Trust 2001
RMID: 0020011530
DOI: 10.1017/S0017089501000039
Published version:
Appears in Collections:Pure Mathematics publications

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