Journal of Nonlinear Mathematical Physics

Volume 9, Issue Supplement 1, February 2002, Pages 14 - 28

A Truncation for Obtaining all the First Degree Birational Transformations of the Painlevé Transcendents

Authors
Robert Conte, Micheline Musette
Corresponding Author
Robert Conte
Received 20 July 2001, Revised 28 August 2001, Accepted 30 August 2001, Available Online 1 February 2002.
DOI
https://doi.org/10.2991/jnmp.2002.9.s1.2How to use a DOI?
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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
9 - Supplement 1
Pages
14 - 28
Publication Date
2002/02/01
ISBN
91-631-2120-4
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2002.9.s1.2How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Robert Conte
AU  - Micheline Musette
PY  - 2002
DA  - 2002/02/01
TI  - A Truncation for Obtaining all the First Degree Birational Transformations of the Painlevé Transcendents
JO  - Journal of Nonlinear Mathematical Physics
SP  - 14
EP  - 28
VL  - 9
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2002.9.s1.2
DO  - https://doi.org/10.2991/jnmp.2002.9.s1.2
ID  - Conte2002
ER  -