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