Wigner Functions versus WKB-Methods in Multivalued Geometrical Optics

dc.creatorSparber, Christof
dc.creatorMarkowich, Peter A.
dc.creatorMauser, Norbert J.
dc.date2001-09-26
dc.date2002-03-20
dc.date.accessioned2026-07-07T04:28:40Z
dc.date.available2026-07-07T04:28:40Z
dc.descriptionWe consider the Cauchy-problem for a class of scalar linear dispersive equations with rapidly oscillating initial data. The problem of high-frequency asymptotics of such models is reviewed,in particular we highlight the difficulties in crossing caustics when using (time-dependent) WKB-methods. Using Wigner measures we present an alternative approach to such asymptotic problems. We first discuss the connection of the naive WKB solutions to transport equations of Liouville type (with mono-kinetic solutions) in the prebreaking regime. Further we show that the Wigner measure approach can be used to analyze high-frequency limits in the post-breaking regime, in comparison with the traditional Fourier integral operator method. Finally we present some illustrating examples.
dc.description38 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0109029
dc.identifierhttp://arxiv.org/abs/math-ph/0109029
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/56871
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subject35Qxx
dc.titleWigner Functions versus WKB-Methods in Multivalued Geometrical Optics
dc.typetext

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