Strong instability of standing waves for nonlinear Schrödinger equations with a delta potential

Abstract

We study strong instability (instability by blowup) of standing wave solutions for a nonlinear Schrödinger equation with an attractive delta potential and $L^2$-supercritical power nonlinearity in one space dimension. We also compare our sufficient condition on strong instability with some known results on orbital instability.

15 pages, 3 figures

References in corpus (2)

• Fast soliton scattering by delta impurities
• Soliton splitting by external delta potentials

Cited by in corpus (2)

• Blow-up and strong instability of standing waves for the NLS-$\delta$ equation on a star graph
• On stability and instability of standing waves for 2d-nonlinear Schrödinger equations with point interaction