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Winter 2008 Instability of standing waves to the inhomogeneous nonlinear Schrödinger equation with harmonic potential
Jianqing Chen, Yue Liu
Illinois J. Math. 52(4): 1259-1276 (Winter 2008). DOI: 10.1215/ijm/1258554361

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 $b \gt 0$.

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Jianqing Chen. Yue Liu. "Instability of standing waves to the inhomogeneous nonlinear Schrödinger equation with harmonic potential." Illinois J. Math. 52 (4) 1259 - 1276, Winter 2008. https://doi.org/10.1215/ijm/1258554361

Information

Published: Winter 2008
First available in Project Euclid: 18 November 2009

zbMATH: 1180.35477
MathSciNet: MR2595766
Digital Object Identifier: 10.1215/ijm/1258554361

Subjects:
Primary: 35A15 , 35B35 , 35J20 , 35Q55

Rights: Copyright © 2008 University of Illinois at Urbana-Champaign

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Vol.52 • No. 4 • Winter 2008
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