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

Reika Fukuizumi, Louis Jeanjean

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)

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 languageEnglish
Pages (from-to)121-136
Number of pages16
JournalDiscrete and Continuous Dynamical Systems
Volume21
Issue number1
Publication statusPublished - 2008 May 1
Externally publishedYes

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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