Quantum Curve and the First Painlevé Equation

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2016
• Main Authors: Iwaki, K., Saenz, A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2016
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147434
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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...