Open Problems for Painlevé Equations

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.

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Cited by in corpus (5)

• 2-parameter $\tau$-function for the first Painlevé equation -Topological recursion and direct monodromy problem via exact WKB analysis-
• Non-Abelian Toda lattice and analogs of Painlevé III equation
• Connection problem of the first Painlevé transcendents with large initial data
• Factorization of Ising correlations C(M,N) for $\nu =-k$ and M+N odd, $M\le N$, $T<T_c$ and their lambda extensions
• Reductions of nonlocal nonlinear Schrödinger equations to Painlevé type functions