%0 Journal Article %A Ferapontov, Evgeny %A Kruglikov, B. %D 2016 %T Dispersionless integrable systems in 3D and Einstein-Weyl geometry %U https://repository.lboro.ac.uk/articles/journal_contribution/Dispersionless_integrable_systems_in_3D_and_Einstein-Weyl_geometry/9561188 %2 https://repository.lboro.ac.uk/ndownloader/files/17193314 %K Formal linearization %K Dispersionless PDEs %K Integrability %K Conformal flatness %K Einstein-Weyl geometry %K Self-duality %K Mechanical Engineering not elsewhere classified %X 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. %I Loughborough University