Stability of standing waves for nonlinear schrödinger equations with critical power nonlinearity and potentials

Reika Fukuizumi

Stability of standing waves for nonlinear schrödinger equations with critical power nonlinearity and potentials

Research output: Contribution to journal › Article

Abstract

We study the stability of standing waves e^iωtφ_ω(x) for a nonlinear Schrödinger equation with critical power nonlinearity |u|^4/nu and a potential V (x) in Rⁿ. Here, ω ∈ R and φ_ω(x) is a ground state of the stationary problem. Under suitable assumptions on V (x), we show that e^iωtφ_ω(x) is stable for sufficiently large ω. This result gives a different phenomenon from the case V (x) = 0 where the strong instability was proved by M. I. Weinstein [25].

Original language	English
Pages (from-to)	259-276
Number of pages	18
Journal	Advances in Differential Equations
Volume	10
Issue number	3
Publication status	Published - 2005 Dec 1
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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Fukuizumi, R. (2005). Stability of standing waves for nonlinear schrödinger equations with critical power nonlinearity and potentials. Advances in Differential Equations, 10(3), 259-276.

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abstract = "We study the stability of standing waves eiωtφω(x) for a nonlinear Schr{\"o}dinger equation with critical power nonlinearity |u|4/nu and a potential V (x) in Rn. Here, ω ∈ R and φω(x) is a ground state of the stationary problem. Under suitable assumptions on V (x), we show that eiωtφω(x) is stable for sufficiently large ω. This result gives a different phenomenon from the case V (x) = 0 where the strong instability was proved by M. I. Weinstein [25].",

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AB - We study the stability of standing waves eiωtφω(x) for a nonlinear Schrödinger equation with critical power nonlinearity |u|4/nu and a potential V (x) in Rn. Here, ω ∈ R and φω(x) is a ground state of the stationary problem. Under suitable assumptions on V (x), we show that eiωtφω(x) is stable for sufficiently large ω. This result gives a different phenomenon from the case V (x) = 0 where the strong instability was proved by M. I. Weinstein [25].

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