30 citations · 70 across the 11 of their papers we have counts for
11 papers
Arrest of blowup for the 3-D semi-relativistic Schrödinger-Poisson system with pseudo-relativistic diffusion
Walid Abou Salem, Thomas Chen, Vitali Vougalter
We show global well-posedness in energy norm of the semi-relativistic Schrödinger-Poisson system of equations with attractive Coulomb interaction in in the presence…
Stochastic acceleration of solitons for the nonlinear Schrödinger equation
Walid K. Abou Salem, Catherine Sulem
The effective dynamics of solitons for the generalized nonlinear Schrödinger equation in a random potential is rigorously studied. It is shown that when the external potential vari…
A remark on the mean-field dynamics of many-body bosonic systems with random interactions
Walid K. Abou Salem
The mean-field limit for the dynamics of bosons with random interactions is rigorously studied. It is shown that, for interactions that are almost-surely bounded, the many-body qua…
Effective Dynamics of Solitons in the Presence of Rough Nonlinear Perturbations
Walid K. Abou Salem
The effective long-time dynamics of solitary wave solutions of the nonlinear Schrödinger equation in the presence of rough nonlinear perturbations is rigorously studied. It is show…
Solitary wave dynamics in time-dependent potentials
Walid K. Abou Salem
We rigorously study the long time dynamics of solitary wave solutions of the nonlinear Schrödinger equation in {\it time-dependent} external potentials. To set the stage, we first…
On the Fluctuations of Macroscopic Observables in Quantum Nonequilibrium Steady States
Walid K. Abou Salem
The fluctuations of macroscopic observables in quantum systems which are in a nonequilibrium steady state are studied rigorously in the thermodynamic limit. In particular, the none…