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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Isospectral deformation of the reduced quasi-classical self-dual Yang–Mills equation

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TLDR
The ‘universal’ character of this novel equation of vanishing Pfaffian type is demonstrated by retrieving and generalizing to higher dimensions a great variety of well-known integrable equations such as the dispersionless Kadomtsev–Petviashvili and Hirota equations and various avatars of the heavenly equation governing self-dual Einstein spaces.
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