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 |
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| Date: | 2019 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2019
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| 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| _version_ | 1862751050353606656 |
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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.
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| first_indexed | 2025-12-07T21:24:16Z |
| format | Article |
| fulltext | |
| 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 |