title: |
A Truncation for Obtaining all the First Degree Birational Transformations of the Painlevé Transcendents |
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publication: |
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| volume-issue: | 9 - Supplement 1 | |
| pages: | 14 - 28 | |
ISSN: |
1402-9251 | |
DOI: |
doi:10.2991/jnmp.2002.9.s1.2 (how to use a DOI) | |
author(s): |
Robert CONTE, Micheline MUSETTE |
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publication date: |
February 2002 |
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abstract: |
A birational transformation is one which leaves invariant an ordinary differential eqution, only changing its parameters. We first recall the consistent truncation which has
allowed us to obtain the first degree birational transformation of Okamoto for the mater Painlevé equation P6. Then we improve it by adding a preliminary step, which
is to find all the Riccati subequations of the considered Pn before performing the
truncation. We discuss in some detail the main novelties of our method, taking as an
example the simplest Painlevé equation for that purpose, P2. Finally, we apply the
method to P5 and obtain its two inequivalent first degree birational transformations. |
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copyright: |
©
Atlantis Press. This article is distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |