Nonlinear instability of linearly unstable standing waves for nonlinear Schr\"odinger equations
Abstract
We study the instability of standing waves for nonlinear Schr\"odinger 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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