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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…
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 , we…
On spatial decay for coherent states of the Benjamin-Ono equation
Gavin Stewart
We consider solutions to the Benjamin-Ono equation that are localized in a reference frame moving to the right with constant…
Asymptotics for the cubic 1D NLS with a slowly decaying potential
Gavin Stewart
We consider the asymptotics of the one-dimensional cubic nonlinear Schrödinger equation with an external potential that does not admit bound states. Assuming that $\jBra{x}^{2+…
Scattering and localized states for defocusing nonlinear Schrödinger equations with potential
Avy Soffer, Gavin Stewart
We study the large-time behavior of global energy class () solutions of the one-dimensional nonlinear Schrödinger equation with a general localized potential term and a defocu…