Wigner Functions versus WKB-Methods in Multivalued Geometrical Optics
| dc.creator | Sparber, Christof | |
| dc.creator | Markowich, Peter A. | |
| dc.creator | Mauser, Norbert J. | |
| dc.date | 2001-09-26 | |
| dc.date | 2002-03-20 | |
| dc.date.accessioned | 2026-07-07T04:28:40Z | |
| dc.date.available | 2026-07-07T04:28:40Z | |
| dc.description | We 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.description | 38 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0109029 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0109029 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56871 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Qxx | |
| dc.title | Wigner Functions versus WKB-Methods in Multivalued Geometrical Optics | |
| dc.type | text |