Wave equation with slowly decaying potential: asymptotics and wave operators

Details Wave equation with slowly decaying potential: asymptotics and wave operators Wave equation with slowly decaying potential: asymptotics and wave operators

2009-08-21

arxiv.org/abs/0908.3210v1

Mathematics

Analysis of PDEs

Scientific paper

For the one-dimensional case, we establish the long-time asymptotics of
solution to Cauchy problem and prove existence of modified wave operators. In
particular, we show that the part of the wave travels ballistically if the
potential is square summable and this result is sharp.

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