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

Pages: 525 - 544, Volume 7, Issue 3, July 2001

doi:10.3934/dcds.2001.7.525       Abstract        Full Text (251.3K)       Related Articles

Reika Fukuizumi - Mathematical institute, Tohoku University, Sendai Miyagi JAPAN, 980-8578, Japan (email)

Abstract: 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:  Nonlinear Schrödinger equation, harmonic potential, standing wave, orbital stability.
Mathematics Subject Classification:   35Q55, 35B35, 35A15.

Received: April 2000;      Revised: January 2001;      Published: April 2001.