Geodesic
A scattering problem in laminar media
Sbornik. Mathematics, Tome 43 (1982) no. 3, pp. 427-441 Cet article a éte moissonné depuis la source Math-Net.Ru

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The scattering problem in a laminar medium $$ \Delta u(x)+k^2q(x_1,\dots,x_n,x_1/\varepsilon)u(x)=0 $$ with a radiation condition at infinity is considered. The potential $q(x,y)$ is periodic in the variable $y$. Here $k$ is a large parameter, and $\varepsilon$ is a small parameter with $k\sim\varepsilon^{-\alpha}$, $\alpha>1$. In this paper a formal asymptotic expansion of the solution of this problem is found. To construct it an operator analogous to the canonical Maslov operator is used which acts on a certain Lagrangian manifold not depending on $\varepsilon$. An analogous problem for the Schrödinger equation in a laminar medium is solved. Bibliography: 10 titles. 
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     title = {A~scattering problem in laminar media},
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A. L. Piatnitski. A scattering problem in laminar media. Sbornik. Mathematics, Tome 43 (1982) no. 3, pp. 427-441. http://geodesic.mathdoc.fr/item/SM_1982_43_3_a9/

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