Gavin Stewart

collaborators

4 papers

math.AP2026

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…

math.AP2025

Weakly localized states of one dimensional Schrodinger equations have localized energy

Gavin Stewart, Avy Soffer

We study the asymptotics of the SchrÃ¶dinger equation with time-dependent potential in dimension one. Assuming that the potential decays sufficiently rapidly as $∣ x ∣ \to \infty$ , w…

math.AP2025

Scattering and localized states for defocusing nonlinear SchrÃ¶dinger equations with potential

Avy Soffer, Gavin Stewart

We study the large-time behavior of global energy class ( $H^{1}$ ) solutions of the one-dimensional nonlinear SchrÃ¶dinger equation with a general localized potential term and a defoc…

math.AP2025

On spatial decay for coherent states of the Benjamin-Ono equation

Gavin Stewart

We consider solutions to the Benjamin-Ono equation $\partial_{t} u - H \partial_{x}^{2} u = - \partial_{x} (u^{2})$ that are localized in a reference frame moving to the right with constant…