18 papers
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…
A Microlocal Open-Boundary Method for Residual-Based Wave Solvers on Unbounded Domains
Avy Soffer, Nguyen Gia Hien, Minh-Binh Tran
We introduce a microlocal phase-space-filtered physics-informed neural network (PINN--TDPSF or Microlocal PINNFilter) framework for wave propagation on unbounded domains. The metho…
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 Trotter Error in Many-body Quantum Dynamics with Coulomb Potentials
Di Fang, Xiaoxu Wu, Avy Soffer
Efficient simulation of many-body quantum systems is central to advances in physics, chemistry, and quantum computing, with a key question being whether the simulation cost scales…