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dc.contributor.authorBerjawi, S.
dc.contributor.authorFerapontov, E.V.
dc.contributor.authorKruglikov, Boris
dc.contributor.authorNovikov, V.S.
dc.date.accessioned2022-01-21T12:54:53Z
dc.date.available2022-01-21T12:54:53Z
dc.date.issued2021-12-07
dc.description.abstractEinstein–Weyl geometry is a triple (D,g,ω) where D is a symmetric connection, [g] is a conformal structure and ω is a covector such that ∙ connection D preserves the conformal class [g], that is, Dg=ωg; ∙ trace-free part of the symmetrised Ricci tensor of D vanishes. Three-dimensional Einstein–Weyl structures naturally arise on solutions of second-order dispersionless integrable PDEs in 3D. In this context, [g] coincides with the characteristic conformal structure and is therefore uniquely determined by the equation. On the contrary, covector ω is a somewhat more mysterious object, recovered from the Einstein–Weyl conditions. We demonstrate that, for generic second-order PDEs (for instance, for all equations not of Monge–Ampère type), the covector ω is also expressible in terms of the equation, thus providing an efficient ‘dispersionless integrability test’. The knowledge of g and ω provides a dispersionless Lax pair by an explicit formula which is apparently new. Some partial classification results of PDEs with Einstein–Weyl characteristic conformal structure are obtained. A rigidity conjecture is proposed according to which for any generic second-order PDE with Einstein–Weyl property, all dependence on the 1-jet variables can be eliminated via a suitable contact transformation.en_US
dc.identifier.citationBerjawi, Ferapontov, Kruglikov BS, Novikov. Second-Order PDEs in 3D with Einstein–Weyl Conformal Structure. Annales de l'Institute Henri Poincare. Physique theorique. 2021:1-31en_US
dc.identifier.cristinIDFRIDAID 1969186
dc.identifier.doi10.1007/s00023-021-01140-2
dc.identifier.issn1424-0637
dc.identifier.issn1424-0661
dc.identifier.urihttps://hdl.handle.net/10037/23750
dc.language.isoengen_US
dc.publisherSpringeren_US
dc.relation.journalAnnales de l'Institute Henri Poincare. Physique theorique
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2021 The Author(s)en_US
dc.titleSecond-Order PDEs in 3D with Einstein–Weyl Conformal Structureen_US
dc.type.versionpublishedVersionen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


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