Rules of discretization for Painlevé equations

Nonlinear Sciences – Exactly Solvable and Integrable Systems

Scientific paper

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21 pages, no figure, standard Latex, to appear in Theory of nonlinear special functions : the Painlev\'e transcendents, eds. L

Scientific paper

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.

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