Geodesic
Quantum Curve and the First Painlevé Equation
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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Kohei Iwaki; Axel Saenz. Quantum Curve and the First Painlevé Equation. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a10/

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