Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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.

References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/qam/856186
Article copyright: © Copyright 1986 American Mathematical Society

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