Recovering Asymptotics at Infinity of Perturbations of Stratified Media
Journées équations aux dérivées partielles (2000), article no. 2, 9 p.

We consider perturbations of a stratified medium ${ℝ}_{x}^{n-1}×{ℝ}_{y}$, where the operator studied is ${c}^{2}\left(x,y\right)\Delta$. The function $c$ is a perturbation of ${c}_{0}\left(y\right)$, which is constant for sufficiently large $|y|$ and satisfies some other conditions. Under certain restrictions on the perturbation $c$, we give results on the Fourier integral operator structure of the scattering matrix. Moreover, we show that we can recover the asymptotic expansion at infinity of $c$ from knowledge of ${c}_{0}$ and the singularities of the scattering matrix at fixed energy.

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author = {Christiansen, Tanya and Joshi, Mark S.},
title = {Recovering {Asymptotics} at {Infinity} of {Perturbations} of {Stratified} {Media}},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
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Christiansen, Tanya; Joshi, Mark S. Recovering Asymptotics at Infinity of Perturbations of Stratified Media. Journées équations aux dérivées partielles (2000), article  no. 2, 9 p. http://www.numdam.org/item/JEDP_2000____A2_0/

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