Stokes matrices for 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.