35 citations · 57 across the 6 of their papers we have counts for
7 papers
Geometric structure of NLS evolution
Justin Holmer, Maciej Zworski
We clarify the relation between the Hamiltonian and Lagrangian approaches to nonlinear evolution equations, focusing specifically on the nonlinear Schroedinger equation. In particu…
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…
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…
Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on
J. Colliander, J. Holmer, M. Visan +1
We consider the Cauchy problem for a family of semilinear defocusing Schrödinger equations with monomial nonlinearities in one space dimension. We establish global well-posedness a…