Quantum Curve and the First Painlev\'e Equation
Mathematical Physics
2016-02-01 v3 Analysis of PDEs
Classical Analysis and ODEs
math.MP
Exactly Solvable and Integrable Systems
Abstract
We show that the topological recursion for the (semi-classical) spectral curve of the first Painlev\'e equation gives a WKB solution for the isomonodromy problem for . 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].
Cite
@article{arxiv.1507.06557,
title = {Quantum Curve and the First Painlev\'e Equation},
author = {Kohei Iwaki and Axel Saenz},
journal= {arXiv preprint arXiv:1507.06557},
year = {2016}
}