The master Painlev\'e VI heat equation
Mathematical Physics
2015-10-27 v1 Classical Analysis and ODEs
math.MP
Exactly Solvable and Integrable Systems
Abstract
Given the second order scalar Lax pair of the sixth Painlev\'e equation, we build a generalized heat equation with rational coefficients which does not depend any more on the Painlev\'e variable. \'Etant donn\'e la paire de Lax scalaire de la sixi\`eme \'equation de Painlev\'e, nous donnons une construction directe de l'\'equation de la chaleur g\'en\'eralis\'ee \`a coefficients rationnels qui ne d\'epend plus de la variable de Painlev\'e.
Cite
@article{arxiv.1409.1166,
title = {The master Painlev\'e VI heat equation},
author = {Robert Conte and Ivan Dornic},
journal= {arXiv preprint arXiv:1409.1166},
year = {2015}
}
Comments
9 pages, no figure. To appear, Comptes rendus, section mathe'matiques, bilingue