Ferapontov E., Kruglikov B. Integrability of dispersionless PDEs in 3D and Einstein-Weyl geometry, talk at The Workshop on Geometry of PDEs and Integrability, 14-18 October 2013, Teplice nad Becvou, Czech Republic (abstract)

Speaker: Boris Kruglikov

Title: Integrability of dispersionless PDEs in 3D and Einstein-Weyl geometry (joint with Eugene Ferapontov)

Abstract:
For several classes of second order dispersionless PDEs in 3D with nondegenerate symbol we demonstrate that their integrability is equivalent to Einstein-Weyl property of the conformal structure naturally associated with the symbol. Similarly, linearization via a properly chosen equivalence group is equivalent to conformal flatness on the equation. Thus, for these classes, integrability can be seen from the geometry of the formal linearization of the PDE. We'll discuss to which extent this might be true in general.