Stability of standing waves for a nonlinear Schrödinger equation with a repulsive dirac delta potential

Reika Fukuizumi; Louis Jeanjean

Stability of standing waves for a nonlinear Schrödinger equation with a repulsive dirac delta potential

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

Abstract

We consider a stationary nonlinear Schrödinger equation with a repulsive delta-function impurity in one space dimension. This equation admits a unique positive solution and this solution is even. We prove that it is a minimizer of the associated energy on the subspace of even functions of H ¹(ℝ, ℂ), but not on all H¹ (ℝ, ℂ), and study its orbital stability.

Original language	English
Pages (from-to)	121-136
Number of pages	16
Journal	Discrete and Continuous Dynamical Systems
Volume	21
Issue number	1
Publication status	Published - 2008 May 1
Externally published	Yes

Keywords

Dirac delta
Nonlinear Schrödinger equation
Stability
Standing waves
Variational methods

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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abstract = "We consider a stationary nonlinear Schr{\"o}dinger equation with a repulsive delta-function impurity in one space dimension. This equation admits a unique positive solution and this solution is even. We prove that it is a minimizer of the associated energy on the subspace of even functions of H 1(ℝ, ℂ), but not on all H1 (ℝ, ℂ), and study its orbital stability.",

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N2 - We consider a stationary nonlinear Schrödinger equation with a repulsive delta-function impurity in one space dimension. This equation admits a unique positive solution and this solution is even. We prove that it is a minimizer of the associated energy on the subspace of even functions of H 1(ℝ, ℂ), but not on all H1 (ℝ, ℂ), and study its orbital stability.

AB - We consider a stationary nonlinear Schrödinger equation with a repulsive delta-function impurity in one space dimension. This equation admits a unique positive solution and this solution is even. We prove that it is a minimizer of the associated energy on the subspace of even functions of H 1(ℝ, ℂ), but not on all H1 (ℝ, ℂ), and study its orbital stability.

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KW - Nonlinear Schrödinger equation

KW - Stability

KW - Standing waves

KW - Variational methods

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