Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations

Abstract

We study the instability of standing waves for nonlinear Schrödinger 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.

16 pages

Cited by in corpus (1)

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