 98224 Guillot J. C., Ralston J.
 Inverse Scattering at Fixed Energy for Layered Media
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Mar 24, 98

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Abstract. \magnification=1200
\noindent {\bf Inverse Scatterng at Fixed Energy for Layered Media}
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In this article we show that
exponentially decreasing perturbations of the sound speed in a
layered medium can be recovered
from the scattering amplitude at fixed energy. We consider
the unperturbed equation $u _{tt} = c_0^2(x_n)\Delta u$ in
$ R \times R^n$, where $n \geq 3$.
The unperturbed sound speed, $c_0(x_n)$, is
assumed to be bounded, strictly positive,
and constant outside a bounded interval on the real
axis. The perturbed sound speed, $c(x)$, satisfies $c(x)
c_0(x_n) < C\exp(\delta x)$ for some $\delta >0$. Our work
is related to the recent results of H. Isozaki (J. Diff. Eq.{\bf 138})
on the case where $c_0$ takes the constant values $c_+ $ and $c_$ on the
positive and negative halflines, and R. Weder on the case $c_0 =c_+
$ for $x_n>h$, $c_0=c_h$ for $0<x_n<h$, and $c_0=c_$ for $x_n<0$
(IIMASUNAM Preprint 70, November, 1997).
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