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Title: On the Einstein-Weyl and conformal self-duality equations
Authors: Dunajski, M.
Ferapontov, E.V.
Kruglikov, B.
Issue Date: 2015
Publisher: © AIP Publishing LLC.
Citation: DUNAJSKI, M., FERAPONTOV, E.V. and 2015. On the Einstein-Weyl and conformal self-duality equations. Journal of Mathematical Physics, 56 (8), 10pp.
Abstract: The equations governing anti-self-dual and Einstein-Weyl conformal geometries can be regarded as “master dispersionless systems” in four and three dimensions, respectively. Their integrability by twistor methods has been established by Penrose and Hitchin. In this note, we present, in specially adapted coordinate systems, explicit forms of the corresponding equations and their Lax pairs. In particular, we demonstrate that any Lorentzian Einstein-Weyl structure is locally given by a solution to the Manakov-Santini system, and we find a system of two coupled third-order scalar partial differential equations for a general anti-self-dual conformal structure in neutral signature.
Description: Copyright (2015) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics 56, 083501 (2015) and may be found at http://scitation.aip.org/content/aip/journal/jmp/56/8/10.1063/1.4927251.
Version: Published
DOI: 10.1063/1.4927251
URI: https://dspace.lboro.ac.uk/2134/19305
Publisher Link: http://dx.doi.org/10.1063/1.4927251
ISSN: 0022-2488
Appears in Collections:Published Articles (Maths)

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