Dispersionless integrable systems in 3D and Einstein-Weyl geometry
Abstract
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.
Cite
@article{arxiv.1208.2728,
title = {Dispersionless integrable systems in 3D and Einstein-Weyl geometry},
author = {Eugene Ferapontov and Boris Kruglikov},
journal= {arXiv preprint arXiv:1208.2728},
year = {2015}
}
Comments
In this version we add Preliminary Section and the Appendix, where we discuss the geometry of PDEs and the method of hydrodynamic reductions. Also we add Lax pairs for the 5 integrable equations of type I, and supply the ancillary files (Maple verifications of the calculations, Maple and Mathematica form of Integrability Conditions, together with their PDF versions) for completeness