Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations

Vladimir Georgiev; Masahito Ohta

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arXiv · 1009.5184

Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations

Vladimir Georgiev·Masahito Ohta

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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.

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Vladimir Georgiev, Masahito Ohta. 2010-09-27. Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations. https://arxiv.org/abs/1009.5184

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