Open Problems for Painlevé Equations
arXiv:1901.10122 · doi:10.3842/SIGMA.2019.006
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.
References in corpus (7)
- Some Open Problems in Random Matrix Theory and the Theory of Integrable Systems. II
- Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painleve' Equation: II
- Solving Local Equivalence Problems with the Equivariant Moving Frame Method
- Differential invariants of 2--order ODEs, I
- Location of Poles for the Hastings-McLeod Solution to the Second Painlevé Equation
- On the quasi-Ablowitz-Segur and quasi-Hastings-McLeod solutions of the inhomogeneous Painlevé II equation
- Theory of light-matter interaction in nematic liquid crystals and the second Painlevé equation