Quantum Curve and the First Painlevé Equation
We show that the topological recursion for the (semi-classical) spectral curve of the first Painlevé equation PI gives a WKB solution for the isomonodromy problem for PI. In other words, the isomonodromy system is a quantum curve in the sense of [Dumitrescu O., Mulase M., Lett. Math. Phys. 104 (2014...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2016 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147434 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Quantum Curve and the First Painlevé Equation / K. Iwaki, A. Saenz // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 36 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-147434 |
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Iwaki, K. Saenz, A. 2019-02-14T18:33:32Z 2019-02-14T18:33:32Z 2016 Quantum Curve and the First Painlevé Equation / K. Iwaki, A. Saenz // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 36 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 34M55; 81T45; 34M60; 34M56 DOI:10.3842/SIGMA.2016.011 https://nasplib.isofts.kiev.ua/handle/123456789/147434 We show that the topological recursion for the (semi-classical) spectral curve of the first Painlevé equation PI gives a WKB solution for the isomonodromy problem for PI. In other words, the isomonodromy system is a quantum curve in the sense of [Dumitrescu O., Mulase M., Lett. Math. Phys. 104 (2014), 635-671, arXiv:1310.6022] and [Dumitrescu O., Mulase M., arXiv:1411.1023]. The authors are grateful to Motohico Mulase for many valuable comments, discussion and continuous encouragements. They also thank Olivia Dumitrescu and Bertrand Eynard for helpful comments. K.I. work is supported by the JSPS for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers “Mathematical Science of Symmetry, Topology and Moduli, Evolution of International Research Network based on Osaka City University Advanced Mathematical Institute (OCAMI)”. A.S. work is supported by UC Davis under the Graduate Research Mentorship fellowship. This article is written during the K.I. stay at The University of California, Davis. K.I. would also like to thank the institute for its support and hospitality. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quantum Curve and the First Painlevé Equation Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Quantum Curve and the First Painlevé Equation |
| spellingShingle |
Quantum Curve and the First Painlevé Equation Iwaki, K. Saenz, A. |
| title_short |
Quantum Curve and the First Painlevé Equation |
| title_full |
Quantum Curve and the First Painlevé Equation |
| title_fullStr |
Quantum Curve and the First Painlevé Equation |
| title_full_unstemmed |
Quantum Curve and the First Painlevé Equation |
| title_sort |
quantum curve and the first painlevé equation |
| author |
Iwaki, K. Saenz, A. |
| author_facet |
Iwaki, K. Saenz, A. |
| publishDate |
2016 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We show that the topological recursion for the (semi-classical) spectral curve of the first Painlevé equation PI gives a WKB solution for the isomonodromy problem for PI. In other words, the isomonodromy system is a quantum curve in the sense of [Dumitrescu O., Mulase M., Lett. Math. Phys. 104 (2014), 635-671, arXiv:1310.6022] and [Dumitrescu O., Mulase M., arXiv:1411.1023].
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147434 |
| citation_txt |
Quantum Curve and the First Painlevé Equation / K. Iwaki, A. Saenz // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 36 назв. — англ. |
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2025-12-07T21:13:24Z |
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2025-12-07T21:13:24Z |
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