307 citations · 1.2k across the 45 of their papers we have counts for
4 papers · 1 filter
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…
Soliton splitting by external delta potentials
Justin Holmer, Jeremy Marzuola, Maciej Zworski
We show that a soliton scattered by an external delta potential splits into two solitons and a radiation term. Theoretical analysis gives the amplitudes and phases of the reflected…
Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrödinger systems
Jim Colliander, Justin Holmer, Nikolaos Tzirakis
We prove low-regularity global well-posedness for the 1d Zakharov system and 3d Klein-Gordon-Schrödinger system, which are systems in two variables $u:\mathbb{R}_x^d\times \mathbb{…
Fast soliton scattering by delta impurities
Justin Holmer, Jeremy Marzuola, Maciej Zworski
We study the Gross-Pitaevskii equation (nonlinear Schroedinger equation) with a repulsive delta function potential. We show that a high velocity incoming soliton is split into a tr…