Volume 9, Issue Supplement 1, February 2002, Pages 14 - 28
A Truncation for Obtaining all the First Degree Birational Transformations of the Painlevé Transcendents
Robert Conte, Micheline Musette
Received 20 July 2001, Revised 28 August 2001, Accepted 30 August 2001, Available Online 1 February 2002.
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- 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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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 -