Rules of discretization for Painlev\'e equations
solv-int
2007-05-23 v1 Exactly Solvable and Integrable Systems
Abstract
The discrete Painlev\'e property is precisely defined, and basic discretization rules to preserve it are stated. The discrete Painlev\'e test is enriched with a new method which perturbs the continuum limit and generates infinitely many no-log conditions. A general, direct method is provided to search for discrete Lax pairs.
Keywords
Cite
@article{arxiv.solv-int/9803014,
title = {Rules of discretization for Painlev\'e equations},
author = {R. Conte and M. Musette},
journal= {arXiv preprint arXiv:solv-int/9803014},
year = {2007}
}
Comments
21 pages, no figure, standard Latex, to appear in Theory of nonlinear special functions : the Painlev\'e transcendents, eds. L. Vinet and P. Winternitz (Springer, Berlin, 1998). Proceedings of Montreal, 13--17 May 1996