Truncation-type methods and Bäcklund transformations for ordinary differential equations: The third and fifth Painlevé equations
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(Published version)
Date
2001
Authors
Gordoa, Pilar
Joshi, Nalini
Pickering, Andrew
Editors
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Journal Title
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Volume Title
Type:
Journal article
Citation
Glasgow Mathematical Journal, 2001; 43(A):23-32
Statement of Responsibility
P. R. Gordoa, N. Joshi and A. Pickering
Conference Name
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.
School/Discipline
School of Mathematical Sciences
Dissertation Note
Provenance
Published online by Cambridge University Press 19 Jul 2002
Description
Additional volume of selected papers from a Conference on Integrable Systems, Islay 1999
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© Glasgow Mathematical Journal Trust 2001