dc.contributor.author Banica, V. dc.contributor.author Vega, L. dc.date.accessioned 2020-02-20T16:13:28Z dc.date.available 2020-02-20T16:13:28Z dc.date.issued 2020-02-05 dc.identifier.uri http://hdl.handle.net/20.500.11824/1087 dc.description.abstract The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schr ̈odinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. Finally we prove the existence of a unique solution of the binormal flow with datum a polygonal line. This equation is used as a model for the vortex filaments dynamics in 3-D fluids and superfluids. We also construct solutions of the binormal flow that present an intermittency phenomena. Finally, the solution we construct for the binormal flow is continued for negative times, yielding a geometric way to approach the continuation after blow-up for the 1-D cubic nonlinear Schr ̈odinger equation. en_US dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Vortex filaments en_US dc.subject Binormal Flow en_US dc.subject nonlinear Schrödinger equations en_US dc.subject Singular data en_US dc.subject talbot effect en_US dc.title Evolution of Polygonal Lines by the Binormal Flow en_US dc.type info:eu-repo/semantics/article en_US dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/669689 en_US dc.relation.projectID ES/1PE/SEV-2017-0718 en_US dc.relation.projectID ES/2PE/PGC2018-094528-B-I00 en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/acceptedVersion en_US dc.journal.title Springer Nature Switzerland AG 2020 en_US
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