Caustics, Catastrophes and Wave Fields

Yu. A. Kravtsov, Yu. I. Orlov (auth.)3540642277, 9783540642275

Caustics, Catastrophes and Wave Fields in a sense continues the treatment of the earlier volume 6 “Geometrical Optics of Inhomogeneous Media” in the present book series, by analysing caustics and their fields on the basis of modern catastrophe theory. This volume covers the key generalisations of geometrical optics related to caustic asymptotic expansions: The Lewis-Kravtsov method of standard functions, Maslov’s method of caonical operators, Orlov’s method of interference integrals, as well as their modifications for penumbra, space-time, random and other types of caustics. All the methods are amply illustrated by worked problems concerning relevant wave-field applications.

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Table of contents :
Front Matter….Pages I-XII
Introduction….Pages 1-7
Rays and Caustics….Pages 8-33
Caustics as Catastrophes….Pages 34-47
Typical Integrals of Catastrophe Theory….Pages 48-72
Uniform Caustic Asymptotics Derived with Standard Integrals….Pages 73-115
Maslov’s Method of the Canonical Operator….Pages 116-128
Method of Interference Integrals….Pages 129-141
Penumbra Caustics….Pages 142-153
Modifications and Generalizations of Standard Integrals and Functions….Pages 154-183
Caustics Revisited….Pages 184-195
Back Matter….Pages 196-210