High Frequency Wave Propagation

CSIC Building (#406), Seminar Room 4122.
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Gaussian Beams

James Ralston

Department of Mathematics at University of California, Los Angeles

Abstract:  Gaussian Beams are asymptotic solutions to linear hyperbolic equations that concentrate on a single ray in space-time. Their most significant feature is that they exist for all time: single rays cannot produce caustics. Continuous superpositions of Gaussian beams give accurate representations of caustics. This has made gaussian beams useful as approximations in problems with many caustics that are not necessarily of standard type. I will give a fairly concise construction of gaussian beams in a fairly general setting and discuss some recent applications.

[LECTURE SLIDES, Part I]
[LECTURE SLIDES, Part II]