307 citations · 1.2k across the 45 of their papers we have counts for
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On the 2d Zakharov system with L^2 Schrödinger data
Ioan Bejenaru, Sebastian Herr, Justin Holmer +1
We prove local in time well-posedness for the Zakharov system in two space dimensions with large initial data in L^2 x H^{-1/2} x H^{-3/2}. This is the space of optimal regularity…
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…
Breathing patterns in nonlinear relaxation
Justin Holmer, Maciej Zworski
In numerical experiments involving nonlinear solitary waves propagating through nonhomogeneous media one observes "breathing" in the sense of the amplitude of the wave going up and…
Asymptotically linear solutions in H^1 of the 2-d defocusing nonlinear Schroedinger and Hartree equations
Justin Holmer, Nikolaos Tzirakis
In the 2-d setting, given an solution to the linear Schrödinger equation , we prove the existence (but not uniqueness) of an solution $u(t)…
Fast soliton scattering by attractive delta impurities
Kiril Datchev, Justin Holmer
We study the Gross-Pitaevskii equation with an attractive delta function potential and show that in the high velocity limit an incident soliton is split into reflected and transmit…