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Long-range scattering
Avy Soffer, Gavin Stewart, Xiaoxu Wu
We study the scattering problem for a long range potential, which is time dependent. We prove the existence and completeness of the scattering wave operators, and find some propert…
Propagation of Regularity for Schroedinger Equations with Time Dependent Potentials
Avy Soffer
The dynamics of Schrödinger equation with time dependent potentials of general time dependence is considered. It is shown that for localized in space potentials, there is propagat…
On The large Time Asymptotics of Klein-Gordon type equations with General Data
Avy Soffer, Xiaoxu Wu
We study the Klein-Gordon equation with general interaction terms, which may be linear or nonlinear, and space-time dependent. We initiate the study of such equations with large (n…
On the Existence of Self-Similar solutions for some Nonlinear Schrödinger equations
Avy Soffer, Xiaoxu Wu
We construct solutions of Schrödinger equations which are asymptotically self-similar solutions as time goes to infinity. Also included are situations with two bubbles. These solu…
On The large Time Asymptotics of Schrödinger type equations with General Data
Avy Soffer, Xiaoxu Wu
For the Schrödinger equation with a general interaction term, which may be linear or nonlinear, time dependent and including charge transfer potentials, we prove the global soluti…
Weakly localized states of one dimensional Schrodinger equations have localized energy
Gavin Stewart, Avy Soffer
We study the asymptotics of the Schrödinger equation with time-dependent potential in dimension one. Assuming that the potential decays sufficiently rapidly as , w…