Supplementary material from "Second-order PDEs in four dimensions with half-flat conformal structure"
Posted on 2020-01-02 - 08:40
We study second-order 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 nontrivial dispersionless Lax pair, our result explains the observation that all known scalar second-order integrable dispersionless PDEs in dimensions four and higher are of Monge–Ampère type. Some partial classification results of Monge–Ampère equations in four dimensions with half-flat conformal structure are also obtained.
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Berjawi, S.; Ferapontov, E.V.; Kruglikov, B.; Novikov, V. (2020). Supplementary material from "Second-order PDEs in four dimensions with half-flat conformal structure". The Royal Society. Collection. https://doi.org/10.6084/m9.figshare.c.4803228.v1
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AUTHORS (4)
SB
S. Berjawi
EF
E.V. Ferapontov
BK
B. Kruglikov
VN
V. Novikov