### Numerical computation of soliton dynamics for NLS equations in a driving potential.

Caliari, Marco, Squassina, Marco (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Caliari, Marco, Squassina, Marco (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Justin Holmer, Jeremy Marzuola, Maciej Zworski (2006)

Journées Équations aux dérivées partielles

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Benoit Pausader (2008)

Journées Équations aux dérivées partielles

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Laurent Michel (2005)

Journées Équations aux dérivées partielles

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In this note, we study the scattering amplitude for the Schrödinger equation with constant magnetic field. We consider the case where the strengh of the magnetic field goes to infinity and we discuss the competition between the magnetic and the electrostatic effects.

Durhuus, Bergfinnur, Gayral, Victor (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Jean-François Bony, Laurent Michel (2003)

Journées équations aux dérivées partielles

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We obtain some microlocal estimates of the resonant states associated to a resonance ${z}_{0}$ of an $h$-differential operator. More precisely, we show that the normalized resonant states are $\mathcal{O}(\sqrt{|\mathrm{Im}\phantom{\rule{0.166667em}{0ex}}{z}_{0}|/h}$ $+{h}^{\infty})$ outside the set of trapped trajectories and are $\mathcal{O}\left({h}^{\infty}\right)$ in the incoming area of the phase space. As an application, we show that the residue of the scattering amplitude of a Schrödinger operator is small in some directions under an estimate of the norm of the spectral projector. Finally we prove...

Jean-François Bony, Setsuro Fujiié, Thierry Ramond, Maher Zerzeri (2011)

Annales de l’institut Fourier

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We study the spectral projection associated to a barrier-top resonance for the semiclassical Schrödinger operator. First, we prove a resolvent estimate for complex energies close to such a resonance. Using that estimate and an explicit representation of the resonant states, we show that the spectral projection has a semiclassical expansion in integer powers of $h$, and compute its leading term. We use this result to compute the residue of the scattering amplitude at such a resonance. Eventually,...