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dc.contributor.authorBerjawi, S.
dc.contributor.authorFerapontov, Eugene V.
dc.contributor.authorKruglikov, Boris
dc.contributor.authorNovikov, Vladimir S
dc.date.accessioned2023-09-11T10:52:43Z
dc.date.available2023-09-11T10:52:43Z
dc.date.issued2020-01-29
dc.description.abstractWe 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 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.en_US
dc.identifier.citationBerjawi, Ferapontov, Kruglikov, Novikov. Second-order PDEs in four dimensions with half-flat conformal structure. Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. 2020;476(2233)en_US
dc.identifier.cristinIDFRIDAID 1842583
dc.identifier.doi10.1098/rspa.2019.0642
dc.identifier.issn1364-5021
dc.identifier.issn1471-2946
dc.identifier.urihttps://hdl.handle.net/10037/30904
dc.language.isoengen_US
dc.publisherThe Royal Societyen_US
dc.relation.journalProceedings of the Royal Society. Mathematical, Physical and Engineering Sciences
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2020 The Author(s)en_US
dc.titleSecond-order PDEs in four dimensions with half-flat conformal structureen_US
dc.type.versionacceptedVersionen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


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