## Illinois Journal of Mathematics

### Instability of standing waves to the inhomogeneous nonlinear Schrödinger equation with harmonic potential

#### Abstract

We study the instability of standing-wave solutions $e^{i\omega t}\phi_{\omega}(x)$ to the inhomogeneous nonlinear Schrödinger equation $i\varphi_t=-\triangle\varphi+|x|^2\varphi-|x|^b|\varphi |^{p-1}\varphi, \quad x\in\mathbb{R}^N,$ where $b \gt 0$ and $\phi_{\omega}$ 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 $b \gt 0$.

#### Article information

Source
Illinois J. Math., Volume 52, Number 4 (2008), 1259-1276.

Dates
First available in Project Euclid: 18 November 2009

https://projecteuclid.org/euclid.ijm/1258554361

Digital Object Identifier
doi:10.1215/ijm/1258554361

Mathematical Reviews number (MathSciNet)
MR2595766

Zentralblatt MATH identifier
1180.35477

#### Citation

Chen, Jianqing; Liu, Yue. Instability of standing waves to the inhomogeneous nonlinear Schrödinger equation with harmonic potential. Illinois J. Math. 52 (2008), no. 4, 1259--1276. doi:10.1215/ijm/1258554361. https://projecteuclid.org/euclid.ijm/1258554361

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