Titlebook: Caustics, Catastrophes and Wave Fields; Yu. A. Kravtsov,Yu. I. Orlov Book 19931st edition Springer-Verlag Berlin Heidelberg 1993 acoustics

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https://doi.org/10.1007/978-3-7643-8994-9 family of wavelets, Orlov’s method becomes Maslov’s method. This chapter also considers Orlov’s interference integrals in which partial wavelets are caustic fields (Airy asymptotics or more complex expansions).

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Book 19931st edition 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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https://doi.org/10.1007/978-3-642-97491-5acoustics; asymptotics; caustics; geometrical optics; optics; uniform caustics

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Observability for Parabolic Equations,Until recently caustics have been treated predominantly on an elementary level like geometrical objects—the envelopes of families of rays. However, physical measurements treat caustics as wave objects, namely, diffuse regions with enhanced amplitude of the wave field.

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Observation for the Wave Equation,This method evolved from a very simple idea of describing the asymptotic of the field first in a mixed coordinate-momentum space and performing the Fourier transformation next in the configuration space. This idea proved to be extremely fruitful and effective, and leads to the formulation of heuristic applicability conditions of Maslov’s method.

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Observability for Parabolic Equations,The standard integrals derived in the catastrophe theory do not exhaust the list of standard functions suitable for a description of caustic fields. In this chapter we reflect on the immense possibilities which mathematics opens up to explore nature.