Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin
We prove that there exists a unique odd meromorphic solution of dP3, u(τ), such that u(0) = 0, and study some of its properties, mainly: the coefficients of its Taylor expansion at the origin and asymptotic behaviour as τ→+∞.
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2019 |
| Main Author: | |
| 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/123456789/210176 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin / A.V. Kitaev // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 13 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862650026052812800 |
|---|---|
| author | Kitaev, A.V. |
| author_facet | Kitaev, A.V. |
| citation_txt | Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin / A.V. Kitaev // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 13 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We prove that there exists a unique odd meromorphic solution of dP3, u(τ), such that u(0) = 0, and study some of its properties, mainly: the coefficients of its Taylor expansion at the origin and asymptotic behaviour as τ→+∞.
|
| first_indexed | 2025-12-07T21:24:38Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210176 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:38Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kitaev, A.V. 2025-12-03T14:25:40Z 2019 Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin / A.V. Kitaev // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 13 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 34M40; 33E17; 34M50; 34M55; 34M60 arXiv: 1809.00122 https://nasplib.isofts.kiev.ua/handle/123456789/210176 https://doi.org/10.3842/SIGMA.2019.046 We prove that there exists a unique odd meromorphic solution of dP3, u(τ), such that u(0) = 0, and study some of its properties, mainly: the coefficients of its Taylor expansion at the origin and asymptotic behaviour as τ→+∞. The author is grateful to P.D. Miller and B.I. Suleimanov for discussions of the papers [1, 11]. The author is indebted to the referees for their significant contribution to improving the quality of the original version of this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin Article published earlier |
| spellingShingle | Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin Kitaev, A.V. |
| title | Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin |
| title_full | Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin |
| title_fullStr | Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin |
| title_full_unstemmed | Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin |
| title_short | Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin |
| title_sort | meromorphic solution of the degenerate third painlevé equation vanishing at the origin |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210176 |
| work_keys_str_mv | AT kitaevav meromorphicsolutionofthedegeneratethirdpainleveequationvanishingattheorigin |