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Caustics, Catastrophes and Wave Fields

Author: Yu A Kravtsov; Yu I Orlov
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 1993.
Series: Springer series on wave phenomena, 15.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
Caustics, Catastrophes and Wave Fields in a sense continues the treatment of the earlier volume 6 "Geometrical Optics of Inhomogeneous Media" by analysing caustics and their fields on the basis of modern catastrophe theory. The present volume covers local and uniform caustic asymptotic expansions: The Lewis-Kravtsov method of standard functions, Maslov's method of canonical operators, Orlov's method of interference  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Yu A Kravtsov; Yu I Orlov
ISBN: 9783642974915 3642974910
OCLC Number: 851363512
Description: 1 online resource (59 illustrations).
Contents: 1 Introduction --
1.1 Caustic Fields in Physical Problems --
1.2 The Geometrical Aspect of the Caustic Problem --
1.3 The Wave Aspect of the Caustic Problem --
2 Rays and Caustics --
2.1 Equations of Geometrical Optics --
2.2 The Role of Rays in the Method of Geometrical Optics --
2.3 Physical Characteristics of Caustics --
2.4 Complex Rays --
3 Caustics as Catastrophes --
3.1 Mappings Induced by Rays --
3.2 Classification of Typical Caustics --
4 Typical Integrals of Catastrophe Theory --
4.1 Standard Caustic Integrals --
4.2 The Airy Integral --
4.3 The Pearsey Integral --
4.4 Other Typical Integrals --
5 Uniform Caustic Asymptotics Derived with Standard Integrals --
5.1 Uniform Airy Asymptotic of a Scalar Field --
5.2 Uniform Caustic Asymptotics Based on General Standard Integrals --
5.3 Illustrative Examples --
6 Maslov's Method of the Canonical Operator --
6.1 Principal Relationships --
6.2 Specific Problems --
7 Method of Interference Integrals --
7.1 Ray Type Integrals --
7.2 Caustic Integrals --
7.3 Additional Topics and Generalizations --
8 Penumbra Caustics --
8.1 Broken Penumbra Caustics --
8.2 Penumbra Caustics of Diffraction Rays --
8.3 Penumbral Caustics and Edge Catastrophes --
9 Modifications and Generalizations of Standard Integrals and Functions --
9.1 Nonpolynomial Phase Standard Integrals --
9.2 Structurally Unstable Caustics --
9.3 Standard Integrals with Amplitude Correction --
9.4 Reflection from a Barrier and Oscillations in a Potential Well --
9.5 Standard Functions Induced by Ordinary Differential Equations --
10 Caustics Revisited --
10.1 Caustics in Dispersive Media --
10.2 Caustics in Anisotropic Media --
10.3 Complex Caustics --
10.4 Random Caustics --
10.5 Caustics in Quantum Mechanical Problems --
10.6 Concluding Remarks --
References --
List of Symbols.
Series Title: Springer series on wave phenomena, 15.
Responsibility: by Yu. A. Kravtsov, Yu. I. Orlov.

Abstract:

Caustics, Catastrophes and Wave Fields in a sense continues the treatment of the earlier volume 6 "Geometrical Optics of Inhomogeneous Media" by analysing caustics and their fields on the basis of modern catastrophe theory. The present volume covers local and uniform caustic asymptotic expansions: The Lewis-Kravtsov method of standard functions, Maslov's method of canonical 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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