Twistor Theory of the Airy Equation
Copyright policy )Twistor Theory of the Airy Equation
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-K��hler metric in its conformal class which we construct explicitly.
Special Issue of SIGMA on Progress in Twistor Theory
- University of Cambridge United Kingdom
High Energy Physics - Theory, Mathematics - Differential Geometry, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematics - Complex Variables, FOS: Physical sciences, twistor theory, Isomonodromic deformations for ordinary differential equations in the complex domain, Airy equation, High Energy Physics - Theory (hep-th), Differential Geometry (math.DG), self-duality, FOS: Mathematics, Twistor theory, double fibrations (complex-analytic aspects), Complex Variables (math.CV), Exactly Solvable and Integrable Systems (nlin.SI)
High Energy Physics - Theory, Mathematics - Differential Geometry, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematics - Complex Variables, FOS: Physical sciences, twistor theory, Isomonodromic deformations for ordinary differential equations in the complex domain, Airy equation, High Energy Physics - Theory (hep-th), Differential Geometry (math.DG), self-duality, FOS: Mathematics, Twistor theory, double fibrations (complex-analytic aspects), Complex Variables (math.CV), Exactly Solvable and Integrable Systems (nlin.SI)
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