First degree birational transformations of the Painlev\'e equations and their contiguity relations
Exactly Solvable and Integrable Systems
2014-06-26 v1
Abstract
We present a consistent truncation, allowing us to obtain the first degree birational transformation found by Okamoto for the sixth Painlev\'e equation. The discrete equation arising from its contiguity relation is then just the sum of six simple poles. An algebraic solution is presented, which is equivalent to but simpler than the Umemura solution. Finally, the well known confluence provides a unified picture of all first degree birational transformations for the lower Painlev\'e equations, ranging them in two distinct sequences.
Keywords
Cite
@article{arxiv.nlin/0110028,
title = {First degree birational transformations of the Painlev\'e equations and their contiguity relations},
author = {Robert Conte and Micheline Musette},
journal= {arXiv preprint arXiv:nlin/0110028},
year = {2014}
}
Comments
LaTex 2e. To appear, J. Phys. A, Special issue SIDE IV