Jianqing Chen, Yue Liu
Published 2008-09-11, updated 2010-10-26Version 5
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. $
Comments: This paper has been withdrawn by the authors. the paper is already published
Continuous dependence of the Cauchy problem for the inhomogeneous nonlinear Schrödinger equation in $H^{s} (\mathbb R^{n} )$
On the Cauchy problem for the inhomogeneous nonlinear Schrödinger equation with inverse-power potential
Local and global well-posedness in $L^{2}(\mathbb R^{n})$ for the inhomogeneous nonlinear Schrödinger equation
![QR code for arXiv:0809.2035 [math.AP]](http://oss.arxitics.com/images/favicon.svg)