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

Reika Fukuizumi

doi:10.3934/dcds.2001.7.525

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2001, Volume 7, Issue 3: 525-544. Doi: 10.3934/dcds.2001.7.525

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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

Received: April 2000

Revised: January 2001

Published: July 2001

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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.

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Mathematics Subject Classification: 35Q55, 35B35, 35A15.

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

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