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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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| Format: | Artikel |
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Інститут математики НАН України
2016
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| Online Zugang: | 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 |
| Zitieren: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862751804454862848 |
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| author | Iwaki, K. Saenz, A. |
| author_facet | Iwaki, K. Saenz, A. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-12-07T21:13:24Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147434 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:13:24Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Quantum Curve and the First Painlevé Equation Iwaki, K. Saenz, A. |
| title | 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_short | Quantum Curve and the First Painlevé Equation |
| title_sort | quantum curve and the first painlevé equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147434 |
| work_keys_str_mv | AT iwakik quantumcurveandthefirstpainleveequation AT saenza quantumcurveandthefirstpainleveequation |