Twistor Theory of the Airy Equation

Abstract

We demonstrate how the complex integral formula for the Airy functions arises from Penrose's twistor contour integral formula. We then use the Lax formulation of the isomonodromy problem with one irregular singularity of order four to show that the Airy equation arises from the anti-self-duality equations for conformal structures of neutral signature invariant under the isometric action of the Bianchi II group. This conformal structure admits a null-Kähler metric in its conformal class which we construct explicitly.

Special Issue of SIGMA on Progress in Twistor Theory

References in corpus (1)

• Anti-self-dual four-manifolds with a parallel real spinor

Cited by in corpus (1)

• Null Kähler geometry and isomonodromic deformations