Nonlinear instability of linearly unstable standing waves for nonlinear Schr\"{o}dinger equations
Analysis of PDEs
2014-08-26 v1
Abstract
We study the instability of standing waves for nonlinear Schr\"{o}dinger equations. Under a general assumption on nonlinearity, we prove that linear instability implies orbital instability in any dimension. For that purpose, we establish a Strichartz type estimate for the propagator generated by the linearized operator around standing wave.
Keywords
Cite
@article{arxiv.1009.5184,
title = {Nonlinear instability of linearly unstable standing waves for nonlinear Schr\"{o}dinger equations},
author = {Vladimir Georgiev and Masahito Ohta},
journal= {arXiv preprint arXiv:1009.5184},
year = {2014}
}
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16 pages