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