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The Quarterly Journal of Mechanics and Applied Mathematics 2003 56(2):187-215; doi:10.1093/qjmam/56.2.187
© 2003 by Oxford University Press
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Diffraction of a Plane Wave by Two Ideal Strips

Andrey V. Shanin1

( 1 Department of Physics, Acoustics, Moscow State University, Leninskie Gory, Moscow 119992, Russia )

The problem of scattering of a plane wave by two strips lying in one plane and having ideal boundary conditions is studied. The following exact results are obtained. (1) The embedding formula is derived. This formula enables to express the far-field diagram, depending on two variables (the angle of incidence and the angle of scattering) as the combination of four functions depending on one variable. (2) The ordinary differential equation with respect to the spectral variable is derived for the components of the far-field diagram. (3) The evolution equations describing the dependance of the far-field diagram on the parameters of the problem (such as the coordinates of the edges of the scatterer) are derived. The results listed above are obtained by applying two independent approaches: the Wiener–Hopf functional equations approach and the diffraction (Schwarzschild's) series approach.

Received 23 November 2001. Revised 18 July 2002.


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