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July  2001, 7(3): 525-544. doi: 10.3934/dcds.2001.7.525

Stability and instability of standing waves for the nonlinear Schrödinger equation with harmonic potential

Reika Fukuizumi 1,

1. 

Mathematical institute, Tohoku University, Sendai Miyagi JAPAN, 980-8578, Japan

Received  April 2000 Revised  January 2001 Published  April 2001

In this paper, we study the stability and the instability of standing waves for the nonlinear Schrödinger equation with harmonic potential. We prove the existence of stable or unstable standing waves under certain conditions on the power of nonlinearity and the frequency of wave.
Keywords: harmonic potential, Nonlinear Schrödinger equation, standing wave, orbital stability..
Mathematics Subject Classification: 35Q55, 35B35, 35A1.
Citation: Reika Fukuizumi. Stability and instability of standing waves for the nonlinear Schrödinger equation with harmonic potential. Discrete and Continuous Dynamical Systems, 2001, 7 (3) : 525-544. doi: 10.3934/dcds.2001.7.525
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