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

Reika Fukuizumi

doi:10.3934/dcds.2001.7.525

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

Reika Fukuizumi

INF - System Information Sciences

Research output: Contribution to journal › Article › peer-review

47 Citations (Scopus)

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.

Original language	English
Pages (from-to)	525-544
Number of pages	20
Journal	Discrete and Continuous Dynamical Systems
Volume	7
Issue number	3
DOIs	https://doi.org/10.3934/dcds.2001.7.525
Publication status	Published - 2001 Jul

Keywords

Harmonic potential
Nonlinear scrödinger equation
Orbital stability
Standing wave

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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title = "Stability and instability of standing waves for the nonlinear Schr{\"o}dinger equation with harmonic potential",

abstract = "In this paper, we study the stability and the instability of standing waves for the nonlinear Schr{\"o}dinger 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 scr{\"o}dinger equation, Orbital stability, Standing wave",

author = "Reika Fukuizumi",

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