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dc.contributor.authorBorrelli, William*
dc.date.accessioned2018-02-19T09:54:02Z
dc.date.available2018-02-19T09:54:02Z
dc.date.issued2017
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17414
dc.language.isoenen
dc.subjectCubic Dirac equationen
dc.subjectDirac equationen
dc.subjectKerr nonlinearityen
dc.subjectstationary solutionsen
dc.subjectgrapheneen
dc.subject.ddc520en
dc.titleStationary solutions for the 2D critical Dirac equation with Kerr nonlinearityen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this paper we prove the existence of an exponentially localized stationary solution for a two-dimensional cubic Dirac equation. It appears as an effective equation in the description of nonlinear waves for some Condensed Matter (Bose-Einstein condensates) and Nonlinear Optics (optical fibers) systems. The nonlinearity is of Kerr-type, that is of the form |ψ| 2 ψ and thus not Lorenz-invariant. We solve compactness issues related to the critical Sobolev embedding H 1 2 (R 2 , C 2) → L 4 (R 2 , C 4) thanks to a particular radial ansatz. Our proof is then based on elementary dynamical systems arguments. Contentsen
dc.relation.isversionofjnlnameJournal of Differential Equations
dc.relation.isversionofjnlvol263en
dc.relation.isversionofjnlissue11en
dc.relation.isversionofjnldate2017-12
dc.relation.isversionofjnlpages7941-7964en
dc.relation.isversionofdoi10.1016/j.jde.2017.08.029en
dc.relation.isversionofjnlpublisherElsevieren
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
hal.person.labIds60*


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