Strong Instability of Standing Waves for Nonlinear Schrödinger Equations with Harmonic Potential

• Ohta Masahito

  Tokyo University of Science

Abstract

We study strong instability of standing waves e^iωtφ_ω(x) for nonlinear Schrödinger equations with L²-supercritical nonlinearity and a harmonic potential, where φ_ω is a ground state of the corresponding stationary problem. We prove that e^iωtφ_ω(x) is strongly unstable if ∂_λ²E(φ_ω^λ)|_λ=1 ≤ 0, where E is the energy and v^λ(x) = λ^N/2v(λx) is the L²-invariant scaling.

Journal

• Funkcialaj Ekvacioj

  Funkcialaj Ekvacioj 61 (1), 135-143, 2018

  Division of Functional Equations, The Mathematical Society of Japan

Keywords

• Nonlinear Schrödinger equation
• Harmonic potential
• Standing wave
• Instability
• Blowup

Details

• CRID: 1390001205113969536
• NII Article ID: 130006726035
• DOI: 10.1619/fesi.61.135
• ISSN: 05328721
• Web Site: https://www.jstage.jst.go.jp/article/fesi/61/1/61_135/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed