Rules of discretization for Painlevé equations
arXiv:solv-int/9803014
Abstract
The discrete Painlevé property is precisely defined, and basic discretization rules to preserve it are stated. The discrete Painlevé 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.
21 pages, no figure, standard Latex, to appear in Theory of nonlinear special functions : the Painlevé transcendents, eds. L. Vinet and P. Winternitz (Springer, Berlin, 1998). Proceedings of Montreal, 13--17 May 1996