95 citations · 842 across the 97 of their papers we have counts for
104 papers
Modified Scattering and Asymptotics for Perturbed One-Dimensional Cubic NLS
Vinh Nguyen, Avy Soffer, Truong Vu
We study the long-time dynamics of small solutions to the one-dimensional nonlinear Schrödinger equation \[ i\partial_t v+\partial_x^2v-β\abs{v}^2v +\cW(x)\abs{v}^4v+γi\partial_xv=…
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 propagati…
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…
Dispersive estimates and long-time validity for Bogoliubov dynamics of interacting Bose gases
Phan Thành Nam, Simone Rademacher, Avy Soffer
We consider the Bogoliubov approximation for the many-body quantum dynamics of weakly interacting Bose gases and establish a uniform-in-time validity of the Bogoliubov theory. The…
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…