Soliton scattering by delta impurities

Justin Holmer; Jeremy Marzuola; Maciej Zworski

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Benoit Pausader (2008)

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Structured matrix numerical solution of the nonlinear Schrödinger equation by the inverse scattering transform.

Aricò, Antonio, van der Mee, Cornelis, Seatzu, Sebastiano (2009)

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Simple derivation of quasinormal modes for arbitrary spins.

Khriplovich, Iosif, Ruban, Gennady (2005)

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Microlocalization of resonant states and estimates of the residue of the scattering amplitude

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 $𝒪 (\sqrt{| Im z_{0} | / h}$ $+ h^{\infty})$ outside the set of trapped trajectories and are $𝒪 (h^{\infty})$ 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...

Scattering amplitude for the Schrödinger equation with strong magnetic field

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.

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Gerdjikov, Vladimir S., Kostov, Nikolay A. (2008)

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Znojil, Miloslav (2009)

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