Differential invariants of Einstein-Weyl structures in 3D

Einstein-Weyl structures on a three-dimensional manifold M are given by a system E of PDEs on sections of a bundle over M. This system is invariant under the Lie pseudogroup G of local diffeomorphisms on M. Two Einstein-Weyl structures are locally equivalent if there exists a local diffeomorphism taking one to the other. Our goal is to describe the quotient equation E∕G whose solutions correspond to nonequivalent Einstein-Weyl structures. The approach uses symmetries of the Manakov-Santini integrable system and the action of the corresponding Lie pseudogroup.