Displaying similar documents to “On the scattering in Gevrey classes for the subcritical Hartree and Schrödinger equations”

On solutions of the Schrödinger equation with radiation conditions at infinity : the long-range case

Yannick Gâtel, Dimitri Yafaev (1999)

Annales de l'institut Fourier

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We consider the homogeneous Schrödinger equation with a long-range potential and show that its solutions satisfying some a priori bound at infinity can asymptotically be expressed as a sum of incoming and outgoing distorted spherical waves. Coefficients of these waves are related by the scattering matrix. This generalizes a similar result obtained earlier in the short-range case.

Small data scattering for nonlinear Schrödinger wave and Klein-Gordon equations

Makoto Nakamura, Tohru Ozawa (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Small data scattering for nonlinear Schrödinger equations (NLS), nonlinear wave equations (NLW), nonlinear Klein-Gordon equations (NLKG) with power type nonlinearities is studied in the scheme of Sobolev spaces on the whole space ℝ n with order s < n / 2 . The assumptions on the nonlinearities are described in terms of power behavior p 1 at zero and p 2 at infinity such as 1 + 4 / n ≤ p 1 ≤ p 2 ≤ 1 + 4 / ( n - 2 s ) for NLS and NLKG, and 1 + 4 / ( n - 1 ) ≤ p 1 ≤ p 2 ≤ 1 + 4 / ( n - 2 s ) for NLW.

Asymptotic behavior of scattering amplitudes in semi-classical and low energy limits

Didier Robert, H. Tamura (1989)

Annales de l'institut Fourier

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We study the semi-classical asymptotic behavior as ( h → 0 ) of scattering amplitudes for Schrödinger operators - ( 1 / 2 ) h 2 Δ + V . The asymptotic formula is obtained for energies fixed in a non-trapping energy range and also is applied to study the low energy behavior of scattering amplitudes for a certain class of slowly decreasing repulsive potentials without spherical symmetry.