Ebook: Caustics, Catastrophes and Wave Fields
- Tags: Optics and Electrodynamics, Electrical Engineering, Theoretical Mathematical and Computational Physics, Geophysics/Geodesy, Engineering general
- Series: Springer Series on Wave Phenomena 15
- Year: 1993
- Publisher: Springer Berlin Heidelberg
- Language: English
- pdf
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.
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.
Content:
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
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.
Content:
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
....
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.
Content:
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
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.
Content:
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
....
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