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This article is cited in 1 scientific paper (total in 1 paper)
Twistor Theory of the Airy Equation
Michael Cole, Maciej Dunajski Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
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.
Keywords:
twistor theory; Airy equation; self-duality.
Received: November 28, 2013; in final form March 18, 2014; Published online March 29, 2014
Citation:
Michael Cole, Maciej Dunajski, “Twistor Theory of the Airy Equation”, SIGMA, 10 (2014), 037, 8 pp.
Linking options:
https://www.mathnet.ru/eng/sigma902 https://www.mathnet.ru/eng/sigma/v10/p37
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Abstract page: | 220 | Full-text PDF : | 44 | References: | 35 |
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