Geodesic
Diffraction by grating consisting of screens with different height: new equations
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 43, Tome 422 (2014), pp. 62-89 Cet article a éte moissonné depuis la source Math-Net.Ru

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A 2D problem of diffraction of a plane wave by a grating consisting of screens of different heights is studied. The incident wave travels at a grazing incidence angle. The consideration is held in the parabolic approximation. Screens are supposed to be perfectly absorbing. Edge Green's functions of the problem are introduced. Embedding formula and a spectral equation are proven. An OE-equation for the unknown coefficient of spectral equation is derived. An evolution equation which describes dependence of the edge Green's functions on geometrical parameter of problem(screen height) is derived. An asymptotic estimation of the reflection coefficient is obtained by using the evolution equation. 
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     author = {A. I. Korol'kov and A. V. Shanin},
     title = {Diffraction by grating consisting of screens with different height: new equations},
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A. I. Korol'kov; A. V. Shanin. Diffraction by grating consisting of screens with different height: new equations. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 43, Tome 422 (2014), pp. 62-89. http://geodesic.mathdoc.fr/item/ZNSL_2014_422_a4/

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