Rules of discretization for Painlevé equations

1998/03/18 by Robert Conte, R. Conte, Conte, R. +3
Computer Science · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Numerical methods for differential equations #Optimization and Variational Analysis #nlin.SI #solv-int

paper · pdf · doi:10.48550/arxiv.solv-int/9803014

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

arxiv created 1998/03/18 · openalex publication_date 1998/03/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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