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

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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

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

Received April 2000 Revised January 2001 Published April 2001

Abstract
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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 & Continuous Dynamical Systems - A, 2001, 7 (3) : 525-544. doi: 10.3934/dcds.2001.7.525

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