1208.2728 (E. V. Ferapontov et al.)

Dispersionless integrable systems in 3D and Einstein-Weyl geometry    [PDF]

E. V. Ferapontov, Boris Kruglikov

We demonstrate that the integrability of multi-dimensional PDEs can be seen from the geometry of their formal linearizations. Thus, for several classes of second order dispersionless PDEs that are integrable by the method of hydrodynamic reductions the symbols of their formal linearizations define conformal structures, which must be Einstein-Weyl in 3D and self-dual in 4D.

View original: http://arxiv.org/abs/1208.2728