Show simple item record

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorCOLIN, Mathieu
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorLANNES, David
dc.date.accessioned2024-04-04T03:02:12Z
dc.date.available2024-04-04T03:02:12Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192956
dc.description.abstractEnWe derive various approximations for the solutions of nonlinear hyperbolic systems with fastly oscillating initial data. We first provide error estimates for the so-called slowly varying envelope, full dispersion, and Schrödinger approximations in a Wiener algebra; this functional framework allows us to give precise conditions on the validity of these models; we give in particular a rigorous proof of the ``practical rule'' which serves as a criterion for the use of the slowly varying envelope approximation (SVEA). We also discuss the extension of these models to short pulses and more generally to large spectrum waves, such as chirped pulses. We then derive and justify rigorously a modified Schrödinger equation with improved frequency dispersion. Numerical computations are then presented, which confirm the theoretical predictions.
dc.language.isoen
dc.title.enShort Pulses Approximations in Dispersive Media
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-00201084
hal.version1
hal.audienceNon spécifiée
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00201084v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=COLIN,%20Mathieu&LANNES,%20David&rft.genre=preprint


Files in this item

FilesSizeFormatView

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record