Curves along which plane waves can interfere
Authors:
S. N. Karp and M. Machover
Journal:
Quart. Appl. Math. 35 (1977), 193-201
MSC:
Primary 78.35; Secondary 35L05
DOI:
https://doi.org/10.1090/qam/502940
MathSciNet review:
502940
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Abstract: Partial results are given on a conjecture in inverse scattering theory concerning the interference of two-dimensional plane waves. The conjecture states that an odd number of plane waves of the same frequency can only cancel each other at isolated points and not along a simple continuous curve. It is partially confirmed here for curves which are nearly flat at some point. An analysis is also made for various possible nodes for an even number of plane waves.
- Samuel N. Karp, Far field amplitudes and inverse diffraction theory, Electromagnetic waves, Univ. of Wisconsin Press, Madison, Wis., 1962, pp. 291–300. MR 0129766
- John William Strutt Rayleigh Baron, The Theory of Sound, Dover Publications, New York, N. Y., 1945. 2d ed. MR 0016009
- Leo M. Levine, A uniqueness theorem for the reduced wave equation, Comm. Pure Appl. Math. 17 (1964), 147–176. MR 161030, DOI https://doi.org/10.1002/cpa.3160170203
Samuel N. Karp, Far field amplitudes and inverse diffraction theory, in Electromagnetic waves, ed. R. E. Langer, Univ. of Wisconsin Press, Madison, 1961, 291–300
Lord Rayleigh, The theory of sound, Dover Publications, New York, 1945
Leo M. Levine, A uniqueness theorem for the reduced wave equation, Comm. Pure Appl. Math. 17, 147–175 (1964) (see section 7).
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Article copyright:
© Copyright 1977
American Mathematical Society
