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Symmetry, Integrability and Geometry: Methods and Applications, 2016, Volume 12, 011, 24 pp.
DOI: https://doi.org/10.3842/SIGMA.2016.011 (Mi sigma1093) 		 
This article is cited in 17 scientific papers (total in 17 papers)

Quantum Curve and the First Painlevé Equation

Kohei Iwakia, Axel Saenzb

a Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan
b Department of Mathematics, University of California, Davis, CA 95616-8633, USA
Full-text PDF (487 kB) Citations (17)
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DOI: https://doi.org/10.3842/SIGMA.2016.011
Abstract: We show that the topological recursion for the (semi-classical) spectral curve of the first Painlevé equation $P_I$ gives a WKB solution for the isomonodromy problem for $P_I$. 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].
Keywords: quantum curve; first Painlevé equation; topological recursion; isomonodoromic deformation; WKB analysis.
Received: August 4, 2015; in final form January 22, 2016; Published online January 29, 2016
Bibliographic databases:
Document Type: Article
MSC: 34M55; 81T45; 34M60; 34M56
Language: English
Citation: Kohei Iwaki, Axel Saenz, “Quantum Curve and the First Painlevé Equation”, SIGMA, 12 (2016), 011, 24 pp.
Citation in format AMSBIB
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    		Symmetry, Integrability and Geometry: Methods and Applications
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