Tronquée Solutions of the Third and Fourth Painlevé Equations
Recently, in a paper by Lin, Dai, and Tibboel, it was shown that the third and fourth Painlevé equations have tronquée and tritronquée solutions. We obtain global information about these tronquée and tritronquée solutions. We find their sectors of analyticity, their Borel summed representations in t...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209862 |
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| Zitieren: | Tronquée Solutions of the Third and Fourth Painlevé Equations / X. Xia // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 31 назв. — англ. |
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Xia, X. 2025-11-27T18:02:25Z 2018 Tronquée Solutions of the Third and Fourth Painlevé Equations / X. Xia // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 31 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 34M25; 34M40; 34M55 arXiv: 1803.11230 https://nasplib.isofts.kiev.ua/handle/123456789/209862 https://doi.org/10.3842/SIGMA.2018.095 Recently, in a paper by Lin, Dai, and Tibboel, it was shown that the third and fourth Painlevé equations have tronquée and tritronquée solutions. We obtain global information about these tronquée and tritronquée solutions. We find their sectors of analyticity, their Borel summed representations in these sectors, as well as the asymptotic position of the singularities near the boundaries of the analyticity sectors. We also correct slight errors in the paper mentioned. I am very grateful for the advice and help of Professors Ovidiu Costin and Rodica Costin when I worked on this problem. I also greatly appreciate the referees whose comments helped me improve my paper significantly. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Tronquée Solutions of the Third and Fourth Painlevé Equations Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Tronquée Solutions of the Third and Fourth Painlevé Equations |
| spellingShingle |
Tronquée Solutions of the Third and Fourth Painlevé Equations Xia, X. |
| title_short |
Tronquée Solutions of the Third and Fourth Painlevé Equations |
| title_full |
Tronquée Solutions of the Third and Fourth Painlevé Equations |
| title_fullStr |
Tronquée Solutions of the Third and Fourth Painlevé Equations |
| title_full_unstemmed |
Tronquée Solutions of the Third and Fourth Painlevé Equations |
| title_sort |
tronquée solutions of the third and fourth painlevé equations |
| author |
Xia, X. |
| author_facet |
Xia, X. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
Recently, in a paper by Lin, Dai, and Tibboel, it was shown that the third and fourth Painlevé equations have tronquée and tritronquée solutions. We obtain global information about these tronquée and tritronquée solutions. We find their sectors of analyticity, their Borel summed representations in these sectors, as well as the asymptotic position of the singularities near the boundaries of the analyticity sectors. We also correct slight errors in the paper mentioned.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209862 |
| citation_txt |
Tronquée Solutions of the Third and Fourth Painlevé Equations / X. Xia // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 31 назв. — англ. |
| work_keys_str_mv |
AT xiax tronqueesolutionsofthethirdandfourthpainleveequations |
| first_indexed |
2025-12-07T14:08:31Z |
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2025-12-07T14:08:31Z |
| _version_ |
1850886002068946944 |