# Second-order PDEs in four dimensions with half-flat conformal structure

@article{Berjawi2020SecondorderPI, title={Second-order PDEs in four dimensions with half-flat conformal structure}, author={S. Berjawi and Eugene V. Ferapontov and Boris S. Kruglikov and V. S. Novikov}, journal={Proceedings of the Royal Society A}, year={2020}, volume={476} }

We study second-order partial differential equations (PDEs) in four dimensions for which the conformal structure defined by the characteristic variety of the equation is half-flat (self-dual or anti-self-dual) on every solution. We prove that this requirement implies the Monge–Ampère property. Since half-flatness of the conformal structure is equivalent to the existence of a non-trivial dispersionless Lax pair, our result explains the observation that all known scalar second-order integrable…

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