Del i serien Springer Series on Wave Phenomena

Caustics, Catastrophes and Wave Fields

Inbunden, Engelska, 1998

AvYu.A. Kravtsov,Yu.I. Orlov

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This text, in a sense, continues the treatment of the earlier Volume 6 in the "Springer Series on Wave Phenomena", titled "Geometrical Optics of Inhomogenous Media", by analyzing caustics and their fields on the basis of modern catastrophe theory. This volume covers the key generalizations of geometrical optics related to caustic asymptotic expansions: The Lewis-Kravtsov method of standard functions; Maslov's method of canoncial 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 illustrated by worked problems concerning relevant wave-field applications.

Produktinformation

Utgivningsdatum1998-11-05
Mått155 x 235 x 18 mm
Vikt518 g
FormatInbunden
SpråkEngelska
SerieSpringer Series on Wave Phenomena
Antal sidor216
Upplaga2
FörlagSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN9783540642275
ÖversättareM.G. Edelev, M. G. Edelev

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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.