Please use this identifier to cite or link to this item: http://hdl.handle.net/2440/3572
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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, PilarJoshi, NaliniPickering, 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 ofResponsibility: 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: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=111905&fulltextType=RA&fileId=S0017089501000039 Appears in Collections: Pure Mathematics publications

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