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Dispersionless integrable systems in 3D and Einstein-Weyl geometry

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journal contribution
posted on 2016-02-05, 10:15 authored by Evgeny FerapontovEvgeny Ferapontov, B. Kruglikov
For several classes of second order dispersionless PDEs, we show that the symbols of their formal linearizations define conformal structures which must be Einstein- Weyl in 3D (or self-dual in 4D) if and only if the PDE is integrable by the method of hydrodynamic reductions. This demonstrates that the integrability of these dispersionless PDEs can be seen from the geometry of their formal linearizations.

Funding

We acknowledge financial support from the LMS (BK) and the University of Tromski (EVF) making this collaboration possible.

History

School

  • Mechanical, Electrical and Manufacturing Engineering

Published in

Journal of Differential Geometry

Volume

97

Issue

2

Pages

215 - 254

Citation

FERAPONTOV, E.V. and KRUGLIKOV, B., 2014. Dispersionless integrable systems in 3D and Einstein-Weyl geometry. Journal of Differential Geometry, 97 (2), pp. 215-254.

Publisher

© International Press

Version

  • AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

2013-12-15

Publication date

2014-06-01

Notes

This paper was accepted for publication in the Journal of Differential Geometry. The definitive published version can be found at: http://projecteuclid.org/euclid.jdg/1405447805

ISSN

0022-040X

Language

  • en