Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



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.

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

  • [1] 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 MR 0129766
  • [2] Lord Rayleigh, The theory of sound, Dover Publications, New York, 1945 MR 0016009
  • [3] Leo M. Levine, A uniqueness theorem for the reduced wave equation, Comm. Pure Appl. Math. 17, 147-175 (1964) (see section 7). MR 0161030

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DOI: https://doi.org/10.1090/qam/502940
Article copyright: © Copyright 1977 American Mathematical Society

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