On stability and instability of standing waves for 2d-nonlinear Schrödinger equations with point interaction

Noriyoshi Fukaya*, Vladimir Georgiev, Masahiro Ikeda

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We study existence and stability properties of ground-state standing waves for two-dimensional nonlinear Schrödinger equation with a point interaction and a focusing power nonlinearity. The Schrödinger operator with a point interaction (−Δα)α∈R describes a one-parameter family of self-adjoint realizations of the Laplacian with delta-like perturbation. The operator −Δα always has a unique simple negative eigenvalue eα. We prove that if the frequency of the standing wave is close to −eα, it is stable. Moreover, if the frequency is sufficiently large, we have the stability in the L2-subcritical or critical case, while the instability in the L2-supercritical case.

Original languageEnglish
Pages (from-to)258-295
Number of pages38
JournalJournal of Differential Equations
Volume321
DOIs
Publication statusPublished - 2022 Jun 5

Keywords

  • Instability
  • Nonlinear Schrödinger equation
  • Point interaction
  • Stability
  • Standing wave

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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