Stokes matrices for Airy equations

TL;DR

This paper computes Stokes matrices for generalized Airy equations, demonstrating their regular unipotent nature, using topological methods related to the Fourier-Sato transform of perverse sheaves.

Contribution

It provides a general method to compute Stokes matrices for a broad class of Airy-type equations, including non-rigid cases, expanding understanding of their monodromy properties.

Findings

Stokes matrices are regular unipotent up to formal monodromy.

The approach uses topological computation via Fourier-Sato transform.

Includes classical and non-rigid Airy equations.

Abstract

We compute Stokes matrices for generalised Airy equations and prove that they are regular unipotent (up to multiplication with the formal monodromy). This class of differential equations was defined by Katz and includes the classical Airy equation. In addition, it includes differential equations which are not rigid. Our approach is based on the topological computation of Stokes matrices of the enhanced Fourier-Sato transform of a perverse sheaf due to D'Agnolo, Hien, Morando and Sabbah.