Dispersionless integrable systems in 3D and Einstein-Weyl geometry
journal contribution
posted on 2016-02-05, 10:15 authored by Evgeny FerapontovEvgeny Ferapontov, B. KruglikovFor 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 GeometryVolume
97Issue
2Pages
215 - 254Citation
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 PressVersion
- 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
2013-12-15Publication date
2014-06-01Notes
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/1405447805ISSN
0022-040XPublisher version
Language
- en
