Illinois Journal of Mathematics

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

Jianqing Chen and Yue Liu

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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

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258554361

Digital Object Identifier
doi:10.1215/ijm/1258554361

Mathematical Reviews number (MathSciNet)
MR2595766

Zentralblatt MATH identifier
1180.35477

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35B35: Stability 35A15: Variational methods 35J20: Variational methods for second-order elliptic equations

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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