Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations

Details Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations

2010-09-27

arxiv.org/abs/1009.5184v1

Mathematics

Analysis of PDEs

16 pages

Scientific paper

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.

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