Existence of wave operators with time-dependent modifiers for the Schödinger equations with long-range potentials on scattering manifolds

Details Existence of wave operators with time-dependent modifiers for the Schödinger equations with long-range potentials on scattering manifolds Existence of wave operators with time-dependent modifiers for the Schödinger equations with long-range potentials on scattering manifolds

2012-01-04

arxiv.org/abs/1201.0911v1

Mathematics

Analysis of PDEs

27 pages

Scientific paper

We construct time-dependent wave operators for Schr\"{o}dinger equations with long-range potentials on a manifold $M$ with asymptotically conic structure. We use the two space scattering theory formalism, and a reference operator on a space of the form $\mathbb{R} \times \partial M$, where $\partial M$ is the boundary of $M$ at infinity. We construct exact solutions to the Hamilton-Jacobi equation on the reference system $\mathbb{R} \times \partial M$, and prove the existence of the modified wave operators.

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