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-dualit...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2014 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146810 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Twistor Theory of the Airy Equation / M. Cole, M. Dunajski // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862738144710885376 |
|---|---|
| author | Cole, M. Dunajski, M. |
| author_facet | Cole, M. Dunajski, M. |
| citation_txt | Twistor Theory of the Airy Equation / M. Cole, M. Dunajski // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 14 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T20:03:19Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146810 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:03:19Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Cole, M. Dunajski, M. 2019-02-11T16:05:53Z 2019-02-11T16:05:53Z 2014 Twistor Theory of the Airy Equation / M. Cole, M. Dunajski // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 14 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 32L25; 34M56 DOI:10.3842/SIGMA.2014.037 https://nasplib.isofts.kiev.ua/handle/123456789/146810 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. This paper is a contribution to the Special Issue on Progress in Twistor Theory. The full collection is available
 at http://www.emis.de/journals/SIGMA/twistors.html. 
 MC would like to thank James Bridgwater for the financial support. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Twistor Theory of the Airy Equation Article published earlier |
| spellingShingle | Twistor Theory of the Airy Equation Cole, M. Dunajski, M. |
| title | Twistor Theory of the Airy Equation |
| title_full | Twistor Theory of the Airy Equation |
| title_fullStr | Twistor Theory of the Airy Equation |
| title_full_unstemmed | Twistor Theory of the Airy Equation |
| title_short | Twistor Theory of the Airy Equation |
| title_sort | twistor theory of the airy equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146810 |
| work_keys_str_mv | AT colem twistortheoryoftheairyequation AT dunajskim twistortheoryoftheairyequation |