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.
- Nonlinear Schrödinger equation
- Standing wave
- Strichartz estimate
ASJC Scopus subject areas