Quantum Curve and the First Painlevé Equation

2015/07/31 by Kohei Iwaki, Axel Saenz
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum #Quantum mechanics #Theoretical physics #math-ph #math.AP #math.CA #math.MP #msc:34M55 #msc:34M60 #msc:34M65 #msc:81T45 #nlin.SI

paper · pdf · doi:10.3842/sigma.2016.011

published as SIGMA 12 (2016), 011, 24 pages

arxiv created 2016/01/29 · openalex publication_date 2016/01/29 · arxiv updated 2016/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show that the topological recursion for the (semi-classical) spectral curve of the first Painlev 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.,

Citations

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