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arXiv · 0809.2035

Instability of Standing Waves to the Inhomogeneous Nonlinear Schr\"odinger Equation with Harmonic Potential

Jianqing Chen·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 Schr\"{o}dinger equation $$i\phi_t=-\triangle\phi+|x|^2\phi-|x|^b|\phi|^{p-1}\phi, \qquad \in\mathbb{R}^N, $$ where $ b > 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 > 0. $

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Jianqing Chen, Yue Liu. 2008-09-11. Instability of Standing Waves to the Inhomogeneous Nonlinear Schr\"odinger Equation with Harmonic Potential. https://arxiv.org/abs/0809.2035

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