Abstract
We construct time-dependent wave operators for Schrödinger 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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Communicated by Jan Derezinski.
This work was partly supported by Grant-in-Aid for JSPS Fellows (No. 09J06551).
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Itozaki, S. Existence of Wave Operators with Time-Dependent Modifiers for the Schrödinger Equations with Long-Range Potentials on Scattering Manifolds. Ann. Henri Poincaré 14, 709–736 (2013). https://doi.org/10.1007/s00023-012-0200-1
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DOI: https://doi.org/10.1007/s00023-012-0200-1