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arXiv · 1902.06439

2-parameter $\tau$-function for the first Painlev\'e equation -Topological recursion and direct monodromy problem via exact WKB analysis-

Kohei Iwaki
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Abstract

We show that a 2-parameter family of $\tau$-functions for the first Painlev\'e equation can be constructed by the discrete Fourier transform of the topological recursion partition function for a family of elliptic curves. We also perform an exact WKB theoretic computation of the Stokes multipliers of associated isomonodromy system assuming certain conjectures.

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Kohei Iwaki. 2019-02-18. 2-parameter $\tau$-function for the first Painlev\'e equation -Topological recursion and direct monodromy problem via exact WKB analysis-. https://doi.org/10.1007/s00220-020-03769-2

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