Journal of Nonlinear Mathematical Physics

Volume 10, Issue Supplement 2, December 2003, Pages 107 - 118

On the Lax pairs of the continuous and discrete sixth Painlevé equations

Authors
Robert Conte, Runliang Lin, Micheline Musette
Corresponding Author
Robert Conte
Available Online 1 December 2003.
DOI
https://doi.org/10.2991/jnmp.2003.10.s2.10How to use a DOI?
Abstract
Among the recently found discretizations of the sixth Painlevé equation P6, only the one of Jimbo and Sakai admits a discrete Lax pair, which does establish its integrabiity. However, a subtle restriction in this Lax pair prevents the possibility to generalize it in order to find the other missing Lax pairs. It happens that the same restriction already exists in the matrix Lax pair of Jimbo and Miwa for the continuous P6. In this preliminary article, we remove this last restriction and give a matrix Lax pair for P6 which is traceless, rational in the dependent and independent variables, holomorphic in the monodromy exponents, with four Fuchsian singularities in the complex plane of the spectral parameter. Its only minor drawback is the presence of the apparent singularity which always exists in the scalar Lax pair. Contents
Open Access
This is an open access article distributed under the CC BY-NC license.

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
10 - Supplement 2
Pages
107 - 118
Publication Date
2003/12
ISBN
91-974824-0-4
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2003.10.s2.10How 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  - Runliang Lin
AU  - Micheline Musette
PY  - 2003
DA  - 2003/12
TI  - On the Lax pairs of the continuous and discrete sixth Painlevé equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 107
EP  - 118
VL  - 10
IS  - Supplement 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2003.10.s2.10
DO  - https://doi.org/10.2991/jnmp.2003.10.s2.10
ID  - Conte2003
ER  -