%0 Journal Article
%T Instability of Standing Waves to the Inhomogeneous Nonlinear Schr£żdinger Equation with Harmonic Potential
%A Jianqing Chen
%A Yue Liu
%J Mathematics
%D 2008
%I arXiv
%X 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. $
%U http://arxiv.org/abs/0809.2035v5