dc.contributor.author | Berjawi, S. | |
dc.contributor.author | Ferapontov, E.V. | |
dc.contributor.author | Kruglikov, Boris | |
dc.contributor.author | Novikov, V.S. | |
dc.date.accessioned | 2023-03-14T08:29:18Z | |
dc.date.available | 2023-03-14T08:29:18Z | |
dc.date.created | 2021-12-16T00:59:35Z | |
dc.date.issued | 2021 | |
dc.identifier.citation | Berjawi, S., Ferapontov, E. V., Kruglikov, B. S., & Novikov, V. S. (2022, July). Second-Order PDEs in 3D with Einstein–Weyl Conformal Structure. In Annales Henri Poincaré (Vol. 23, No. 7, pp. 2579-2609). Cham: Springer International Publishing. | en_US |
dc.identifier.issn | 1424-0637 | |
dc.identifier.uri | https://hdl.handle.net/11250/3058065 | |
dc.description.abstract | Einstein–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.language.iso | eng | en_US |
dc.publisher | Springer | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | Second-Order PDEs in 3D with Einstein–Weyl Conformal Structure | en_US |
dc.type | Peer reviewed | en_US |
dc.type | Journal article | en_US |
dc.description.version | publishedVersion | en_US |
dc.rights.holder | The authors | en_US |
dc.subject.nsi | VDP::Matematikk og Naturvitenskap: 400::Fysikk: 430 | en_US |
dc.source.pagenumber | 1-31 | en_US |
dc.source.journal | Annales de l'Institute Henri Poincare. Physique theorique | en_US |
dc.identifier.doi | 10.1007/s00023-021-01140-2 | |
dc.identifier.cristin | 1969186 | |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 1 | |