Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 15 (2019), 006, 20 pages      arXiv:1901.10122      https://doi.org/10.3842/SIGMA.2019.006
Contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications (OPSFA14)

Open Problems for Painlevé Equations

Peter A. Clarkson
School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent, CT2 7FS, UK

Received January 18, 2019; Published online January 29, 2019

Abstract
In this paper some open problems for Painlevé equations are discussed. In particular the following open problems are described: (i) the Painlevé equivalence problem; (ii) notation for solutions of the Painlevé equations; (iii) numerical solution of Painlevé equations; and (iv) the classification of properties of Painlevé equations.

Key words: Painlevé equations; open problems.

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