We consider the acoustic propagator
H=−∇·ρ∇ acting in
L2(Ω) with Ω:=Ω'×\mathbb{R} and Ω' a bounded open set in \mathbb{R}
n−1,
n≥ 2. The real-valued function ρ belongs to
L∞(Ω), and is bounded from below by
c>0. We assume there exist two strictly positive constants
c1 and
c2 and two perturbations, δ
S of short-range type and δ
L of long-range type, such that ρ=
cj+δ
S+δ
L on Ω
j:={(
x',
xn)∈Ω | (−1)
jxn>0},
j=1, 2. We build two modified free evolutions
Uj(
t),
j=1, 2, such that the wave operators Ω
j±:=
s−lim
t→±∞eitHUj(
t),
j=1, 2, exist and are asymptotically complete.
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