Caustics, Catastrophes and Wave Fields / by Yu.A. Kravtsov, Yu.I. Orlov.

Format:

Book

Author/Creator:

Kravtsov, Yu.A., Author.

Orlov, Yu.I., Author.

Series:

Springer Series on Wave Phenomena ; 15

Language:

English

Subjects (All):

Acoustics.

Electrodynamics.

Classical Electrodynamics.

Local Subjects:

Acoustics.

Classical Electrodynamics.

Physical Description:

1 online resource (XII, 216 p.)

Edition:

2nd ed. 1993.

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1993.

Language Note:

English

Summary:

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 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.

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

2.4 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 Pearcey 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

6.3. Generalization by Using Fractional Transformations

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 Penumbra 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

10.3 Complex Caustics

10.4 Random Caustics

10.5 Caustics in Quantum Mechanical Problems

10.6 Concluding Remarks

References

List of Symbols.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

ISBN:

3-642-59887-0