This article is cited in 19 papers

Quantum Curve and the First Painlevé Equation

Kohei Iwaki^a, Axel Saenz<sup>b

a</sup> Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan
^b Department of Mathematics, University of California, Davis, CA 95616-8633, USA

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.

MSC: 34M55; 81T45; 34M60; 34M56

Received: August 4, 2015; in final form January 22, 2016; Published online January 29, 2016

Language: English

DOI: 10.3842/SIGMA.2016.011

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ArXiv: 1507.06557