Open Problems for Painlevé Equations

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 o...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2019
Main Author: Clarkson, P.A.
Format: Article
Language:English
Published: Інститут математики НАН України 2019
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/210069
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Open Problems for Painlevé Equations / P.A. Clarkson // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 146 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Clarkson, P.A.
author_facet Clarkson, P.A.
citation_txt Open Problems for Painlevé Equations / P.A. Clarkson // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 146 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description 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.
first_indexed 2025-12-07T21:24:16Z
format Article
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id nasplib_isofts_kiev_ua-123456789-210069
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T21:24:16Z
publishDate 2019
publisher Інститут математики НАН України
record_format dspace
spelling Clarkson, P.A.
2025-12-02T09:37:51Z
2019
Open Problems for Painlevé Equations / P.A. Clarkson // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 146 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 33E17; 34M55
arXiv: 1901.10122
https://nasplib.isofts.kiev.ua/handle/123456789/210069
https://doi.org/10.3842/SIGMA.2019.006
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.
I would like to thank Mark Ablowitz, Andrew Bassom, Chris Cosgrove, Alfredo Deaño, Percy Deift, Marco Fasondini, Bengt Fornberg, David Gómez-Ullate, Rod Halburd, Andrew Hone, Alexander Its, Kerstin Jordaan, Nalini Joshi, Erik Koelink, Martin Kruskal, Ana Loureiro, Elizabeth Mansfield, Marta Mazzocco, Bryce McLeod, Peter Miller, Walter Van Assche, and André Weideman for their helpful comments and illuminating discussions.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Open Problems for Painlevé Equations
Article
published earlier
spellingShingle Open Problems for Painlevé Equations
Clarkson, P.A.
title Open Problems for Painlevé Equations
title_full Open Problems for Painlevé Equations
title_fullStr Open Problems for Painlevé Equations
title_full_unstemmed Open Problems for Painlevé Equations
title_short Open Problems for Painlevé Equations
title_sort open problems for painlevé equations
url https://nasplib.isofts.kiev.ua/handle/123456789/210069
work_keys_str_mv AT clarksonpa openproblemsforpainleveequations