307 citations · 1.2k across the 45 of their papers we have counts for
5 papers · 2 filters
Scattering for the non-radial 3D cubic nonlinear Schroedinger equation
Thomas Duyckaerts, Justin Holmer, Svetlana Roudenko
Scattering of radial solutions to the 3D focusing cubic nonlinear Schrödinger equation below a mass-energy threshold and satisfying an initial mass-grad…
Soliton interaction with slowly varying potentials
Justin Holmer, Maciej Zworski
We study the Gross-Pitaevskii equation with a slowly varying smooth potential, . We show that up to time and errors of size in , the solutio…
On blow-up solutions to the 3D cubic nonlinear Schroedinger equation
Justin Holmer, Svetlana Roudenko
For the 3d cubic nonlinear Schrödinger (NLS) equation, which has critical (scaling) norms and , we first prove a result establishing sufficient conditions for g…
A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation
Justin Holmer, Svetlana Roudenko
We consider the problem of identifying sharp criteria under which radial (finite energy) solutions to the focusing 3d cubic nonlinear Schrödinger equation (NLS) $i\partial_t…
Slow soliton interaction with delta impurities
Justin Holmer, Maciej Zworski
We study the Gross-Pitaevskii equation with a delta function potential, , where is small, and analyze the solutions for which the initial condition is a soliton with…