UID:
almahu_9949199301402882
Umfang:
online resource.
Ausgabe:
1st ed. 1993.
ISBN:
9783642974915
Serie:
Springer Series on Wave Phenomena, 15
Inhalt:
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.
Anmerkung:
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.
In:
Springer Nature eBook
Weitere Ausg.:
Printed edition: ISBN 9783642974939
Weitere Ausg.:
Printed edition: ISBN 9783540565871
Weitere Ausg.:
Printed edition: ISBN 9783642974922
Sprache:
Englisch
DOI:
10.1007/978-3-642-97491-5
URL:
https://doi.org/10.1007/978-3-642-97491-5
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