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

Noriyoshi Fukaya*, Vladimir Georgiev, Masahiro Ikeda

*この研究の対応する著者

研究成果: Article査読

抄録

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.

本文言語English
ページ(範囲)258-295
ページ数38
ジャーナルJournal of Differential Equations
321
DOI
出版ステータスPublished - 2022 6月 5

ASJC Scopus subject areas

  • 分析
  • 応用数学

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