Instability of Standing Waves to the Inhomogeneous Nonlinear Schrödinger Equation with Harmonic Potential

Details Instability of Standing Waves to the Inhomogeneous Nonlinear Schrödinger Equation with Harmonic Potential Instability of Standing Waves to the Inhomogeneous Nonlinear Schrödinger Equation with Harmonic Potential

2008-09-11

arxiv.org/abs/0809.2035v5

Mathematics

Analysis of PDEs

This paper has been withdrawn by the authors. the paper is already published

Scientific paper

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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