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

Kohei Iwaki

doi:10.1007/s00220-020-03769-2

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

Mathematical Physics 2020-06-24 v4 Analysis of PDEs Classical Analysis and ODEs math.MP Exactly Solvable and Integrable Systems

Authors: Kohei Iwaki

View on arXiv ↗ PDF ↗ DOI ↗

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.

Keywords

special functions

Cite

@article{arxiv.1902.06439,
  title  = {2-parameter $\tau$-function for the first Painlev\'e equation -Topological recursion and direct monodromy problem via exact WKB analysis-},
  author = {Kohei Iwaki},
  journal= {arXiv preprint arXiv:1902.06439},
  year   = {2020}
}

Comments

41 pages, 5 figures, some figures in color, references added in v2, typos are corrected in v3

Related papers

View all related →