Some singular, nonlinear, integral equations arising in physical problems
Author:
I. Lerche
Journal:
Quart. Appl. Math. 44 (1986), 319-326
MSC:
Primary 45G05; Secondary 76Q05, 78A40
DOI:
https://doi.org/10.1090/qam/856186
MathSciNet review:
856186
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Abstract: We show that if $Q$, the logarithmic decrement of plane wave intensity with position, is measured as a function of frequency, then the in-phase and quadrature components of the medium’s characteristic response function (in the form of a dielectric function for electromagnetic waves, an elastic response function for acoustic waves, etc.) satisfy a nonlinear, singular, integral equation with the in-phase and quadrature components connected through a causal Hilbert transform pair.
K. Aki and P. G. Richards, Quantitative seismology, theory and methods, Freeman, San Francisco (1980)
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- John David Jackson, Classical electrodynamics, 2nd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1975. MR 0436782
- Philip M. Morse and Herman Feshbach, Methods of theoretical physics. 2 volumes, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0059774
J. M. Tribolet, Seismic applications of homomorphic signal processing, Prentice-Hall, Englewood Cliffs, N. J. (1979)
- F. G. Tricomi, Integral equations, Pure and Applied Mathematics, Vol. V, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1957. MR 0094665
K. Aki and P. G. Richards, Quantitative seismology, theory and methods, Freeman, San Francisco (1980)
R. Courant and D. Hilbert, Methods of mathematical physics, Interscience, New York (1953)
J. D. Jackson, Classical electrodynamics, Wiley, New York (1962)
P. M. Morse and H. Feshbach, Methods of theoretical physics, McGraw-Hill, New York (1953)
J. M. Tribolet, Seismic applications of homomorphic signal processing, Prentice-Hall, Englewood Cliffs, N. J. (1979)
F. G. Tricomi, Integral equations, Intersciencc, New York (1957)
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Article copyright:
© Copyright 1986
American Mathematical Society