English

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

R2 v1 2026-06-22T05:47:48.679Z