Instability of Standing Waves to the Inhomogeneous Nonlinear Schrödinger Equation with Harmonic Potential

Abstract

We study the instability of standing-wave solutions $e^{i\omega t}{\varphi }_{\omega }(x)$ to the inhomogeneous nonlinear Schrödinger equation $$i{\varphi }_t=-△\varphi +|x{|}^2\varphi -|x{|}^b|\varphi {|}^{p-1}\varphi ,\in {\mathbb{R}}^N,$$ where $b>0$ and ${\varphi }_{\omega }$ is a ground-state solution. The results of the instability of standing-wave solutions reveal a balance between the frequency $\omega$ of wave and the power of nonlinearity $p$ for any fixed $b>0.$

arXiv commentThis paper has been withdrawn by the authors. the paper is already published