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Babich V.M., Buldyrev V.S. — Short-wavelength diffraction theory
Babich V.M., Buldyrev V.S. — Short-wavelength diffraction theory

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Название: Short-wavelength diffraction theory

Авторы: Babich V.M., Buldyrev V.S.

Аннотация:

In the study of short-wave diffraction problems, asymptotic methods - the ray method, the parabolic equation method, and its further development as the "etalon" (model) problem method - play an important role. These are the methods to be treated in this book. The applications of asymptotic methods in the theory of wave phenomena are still far from being exhausted, and we hope that the techniques set forth here will help in solving a number of problems of interest in acoustics, geophysics, the physics of electromagnetic waves, and perhaps in quantum mechanics. In addition, the book may be of use to the mathematician interested in contemporary problems of mathematical physics. Each chapter has been annotated. These notes give a brief history of the problem and cite references dealing with the content of that particular chapter. The main text mentions only those publications that explain a given argument or a specific calculation. In an effort to save work for the reader who is interested in only some of the problems considered in this book, we have included a flow chart indicating the interdependence of chapters and sections. The authors consider it their pleasant duty to thank M.M. Popov, who, at the authors' request, wrote Sects. 10.1-7, and also LA. Molotkov, who was involved in all stages of preparing this book. LA. Molotkov wrote Sect. 7.5 and most of Chap. 11, and was our coauthor in writing Chap. 6. We are indebted to participants at the seminar of the Leningrad Section of the V.A. Steklov Institute of Mathematics and Leningrad State University on the mathematical theory of diffraction, but especially to V.F. Lazutkin, for their constructive criticism. We owe a great deal to the editors of the book. Their careful work, at times going far beyond the limits of direct editorial duties, enabled us to eliminate a number of shortcomings in the manuscript


Язык: en

Рубрика: Математика/Анализ/Асимптотические методы, Теория возмущений/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1972

Количество страниц: 456

Добавлена в каталог: 02.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Airy function of the first kind      400—416
Airy function of the second kind      400—416
Annihilation operator      232 274
Approximate congruence of rays      97
Attenuation function      133 217
Birkhoff series      269
Canonical variables      17
Caustic      3 39
Caustic coordinate system      47
Caustic index      73 76
Caustic sum      363
Caustic sum, approximate      364 365
Caustic, approximate      367
Central field      22
Characteristic of a first-order nonlinear equation      37
Christoffel symbols      247
Closed congruence of rays      68
Conditions for stability of a resonator in the first approximation      261
Contour passing through a caustic against a ray      72
Contour passing through a caustic along a ray      72
Contour passing through a reflecting boundary against a ray      72
Contour passing through a reflecting boundary along a ray      72
Contraction (of a tensor)      418
Contravariant components of a vector      419
Covariant components of a vector      419
Covariant derivative      219
Creation operator      232 274
Cycle, stable in the first approximation      4
Deep shadow zone      392—398
Dielectric constant (permittivity)      29
Diffraction boundary layer      4
Diffraction coefficients      28
Dispersion equation      12
Divergence of a ray field      32 39 56
Divergence of a vector      420 421
Effective radius of curvature of a curve      50 116 132
Eigenfrequencies of an open resonator      211
Eigenfunctions and eigenfrequencies of a multiple mirror resonator      274
Eigenfunctions concentrated in the neighborhood of an extremal ray of a region      180
Eigenfunctions concentrated in the-neighborhood of a closed geodesic      214
Eigenfunctions concentrated near a closed phase trajectory      246
Eigenfunctions concentrated near the boundary of a region, asymptotic      145
Eigenfunctions of a circle      75 146
Eigenfunctions of the exterior of n      168
Eigenvalues of a circle      75
Eigenvalues of the elliptic operator      246
Eigenvalues, bouncing ball type      4 5 91 105
Eigenvalues, bouncing ball type, in the case of variable velocity      121
Eigenvalues, of an ellipse      81
Eigenvalues, whispering gallery type      4 5 91 97 145 161
Eigenvalues, whispering gallery type, asymptotic      135
Eigenvalues, whispering gallery type, in the case of variable velocity      114
Eikonal      2
Eikonal equation      12 19 30
Eikonal equation for surface rays      367
Eikonal, surface      367
Energy density      28 32
Envelope of a ray field      3 42
Etalon function      146
Etalon problem      43 146 180 357
Etalon problem method      5 146
Euler’s equations      16 263
Even polynomial      236 280
Evolute      42 64
Extremal diameter      105
Extremal of a functional      16
Extremal of a functional, Mayer family      67
Extremal polygon      314
Extremal rays      121
Fermat functional      14 19 262
First variation      15
Floquet index      220 268
Floquet solution      220 224 268
Foliated space with m-dimensional vector leaves      219
Fourth-order integral invariant      267
Function concentrated in the neighborhood of a curve      3
Function, Bessel      43
Function, Bessel, Airy function asymptotics of      80 147
Function, Bessel, Debye asymptotics of      43
Fundamental matrix of a system      223
Gaussian curvature      241
Gaussian system of units      29
Generators of a fundamental group      73
Geometrical divergence      19 23
Green’s function for a Riemann surface      301
Green’s function for the exterior of a circle      286
Green’s function for the Helmholtz equation      36 285
Hamilton — Jacobi equation      248
Hamiltonian function      18
Hamiltonian system      18 48 248
Hankel function      35
Hanlcel function, asymptotic series for      36
Held near a caustic      56
Held of a source on the boundary of a circle      326
Held of a surface source (interior problem)      306
Helmholtz equation      1 11 43
Hermite polynomial      142 181 246
Higher-order harmonics      275
Index of intersection (Kronecker — Poincare index)      75
Involute      42 64
Jacobi equation for a geodesic      220
Keller — Rubinow method      3 66
Kronecker symbol      418
Laplacian operator      421
Laplacian operator in curvilinear coordinates      421
Laplacian operator m arbitrary orthogonal coordinates      132
Limiting absorption principle      2 170 306
Linearized Euler equation      189 194 222
Liouville equation      223
Localization principle      38
Locally plane wave      11
Maslov canonical operator      64
Maslov — Arnold index      96
Maxwell’s equations      29
Method of constructive interference      96
Metric tensor      14 33 48 247 419
Minimal diameter of a region      108 130
Monodromy operator      224 266
Multi-sheeted space      68 96
Multidimensional generalized Hermite functions      235
Multiple mirror resonator      258
Multiplier (Hoquet)      224 268
Neutralizer function      176
Neutralizing function      370
Nonconfocal resonator      213
Normal congruence of rays      67
Normal curvature      49
Normal fibering      218
Normal impedance      167
Observation circle      339
Odd polynomial      236 280
One-dimensional cycle (closed chain)      3
One-dimensional cycle (closed chain), extremal      259
One-dimensional cycle (closed chain), oriented      71
Operator with discrete spectrum      173
Optical distance      78
Orthogonal coordinates      132
Parabolic cylinder functions      141 181
Parabolic equation method      4 131
Permeability      29
Phase factor      12
Phase trajectory      246 248
Quantization conditions      73
Radius of curvature of a curve      38 92 98 114
Radius of curvature of an ellipse      92
Radius of torsion of a ray      31
Ray coordinates      19 22
Ray formula for multiply reflected waves      307
Ray method      2 10
Ray method in the small      4 97
Ray method, Maxwell’s equations      29
Ray solution      10
Ray tube      24
Rays      16
Reciprocity principle      298
Reduced arc length      345
Reduced normal      347
Reflection index      73.76
Regular field of rays      2 23
Resonator axis      259
Riemannian curvature      118 119
Riemannian manifold      33 214
Riemannian normal coordinates      215
Riemarm surface of logarithmic type      287
Scalar field      418
Scalar product of vectors      418
Semi-geodesic coordinate system      240
Simple covering of a region      67
Solution of Helmholtz’ equation in a boundary layer      150
Stability of a geodesic in the first approximation      222
Stability of a resonator in the first approximation      267
Surface eikonal equation      367
System of rays stable in the first approximation      98 107
Tensor      417
Tensor field      417
Transport equation      12 26
Transversality condition      19 26
Universal covering      219
Vector field      417
Vector, contravariant      33 417
Vector, covariant      33 417
Vectors, associated      224
Wave equation      1
Wave front      12
Wave front velocity      13
Wave, creeping      170 289
Wave, normal      178
Wave, ray form of      347
Wave, standing      149
Wave, surface      313
Whispering gallery effect      306
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