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Quantum Curve and the First Painlevé Equation
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Quantum Curve and the First Painlevé Equation
Інший ID:
2010 Mathematics Subject Classification: 34M55; 81T45; 34M60; 34M56
DOI:10.3842/SIGMA.2016.011
DOI:10.3842/SIGMA.2016.011
Посилання:
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.
Підтримка:
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.
Дата:
2016
Переглядів:
735
Завантажень:
280
Анотація:
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].
