Orbital stability and uniqueness of the ground state for the non-linear schrödinger equation in dimension one

Daniele Garrisi, Vladimir Georgiev

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We prove that standing-waves which are solutions to the non-linear Schrödinger equation in dimension one, and whose profiles can be obtained as minima of the energy over the mass, are orbitally stable and non-degenerate, provided the non-linear term satisfies a Euler differential inequality. When the non-linear term is a combined pure power-type, then there is only one positive, symmetric minimum of prescribed mass.

Original languageEnglish
Pages (from-to)4309-4328
Number of pages20
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume37
Issue number8
DOIs
Publication statusPublished - 2017 Aug

Keywords

  • Schrödinger
  • Stability
  • uniqueness

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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