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Symmetry, Integrability and Geometry: Methods and Applications, 2014, Volume 10, 037, 8 pp.
DOI: https://doi.org/10.3842/SIGMA.2014.037
(Mi sigma902)
 

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
Full-text PDF (695 kB) Citations (1)
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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
Bibliographic databases:
Document Type: Article
MSC: 32L25; 34M56
Language: English
Citation: Michael Cole, Maciej Dunajski, “Twistor Theory of the Airy Equation”, SIGMA, 10 (2014), 037, 8 pp.
Citation in format AMSBIB
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\by Michael~Cole, Maciej~Dunajski
\paper Twistor Theory of the Airy Equation
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\vol 10
\papernumber 037
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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