On stability and instability of standing waves for the nonlinear Schrödinger equation with an inverse-square potential

DOI10.1063/1.5038041zbMath1402.35255arXiv1805.01245OpenAlexW3103843372MaRDI QIDQ4556604

Shihui Zhu, Abdelwahab Bensouilah, Van Duong Dinh

Publication date: 16 November 2018

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.01245

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Stability in context of PDEs (35B35) Periodic solutions to PDEs (35B10) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (20)

Instability of standing waves for the inhomogeneous Gross-Pitaevskii equation ⋮ On stability and instability of standing waves for the inhomogeneous fractional Schrödinger equation ⋮ Existence of stable standing waves for the nonlinear Schrödinger equation with inverse-power potential and combined power-type and Choquard-type nonlinearities ⋮ Strong instability of standing waves for the nonlinear Schrödinger equation in trapped dipolar quantum gases ⋮ Global existence, blow-up and mass concentration for the inhomogeneous nonlinear Schrödinger equation with inverse-square potential ⋮ Existence of stable standing waves for the fractional Schrödinger equations with combined power-type and Choquard-type nonlinearities ⋮ Existence and stability of standing waves for the inhomogeneous Gross-Pitaevskii equation with a partial confinement ⋮ On nonlinear Schrödinger equations with attractive inverse-power potentials ⋮ Strong instability of standing waves for a fourth-order nonlinear Schrödinger equation with the mixed dispersions ⋮ On the instability of standing waves for the nonlinear Schrödinger equation with inverse-square potential ⋮ Orbital stability of standing waves for Schrödinger type equations with slowly decaying linear potential ⋮ Asymptotic behavior of constraint minimizers for the mass-critical fractional nonlinear Schrödinger equation with a subcritical perturbation ⋮ Stability and instability of standing waves for the fractional nonlinear Schrödinger equations ⋮ On nonlinear Schrödinger equations with repulsive inverse-power potentials ⋮ Existence, non-existence and blow-up behaviour of minimizers for the mass-critical fractional non-linear Schrödinger equations with periodic potentials ⋮ Existence and orbital stability of standing waves to a nonlinear Schrödinger equation with inverse square potential on the half-line ⋮ Semilinear Schrödinger equations with a potential of some critical inverse-square type ⋮ Uniqueness of ground state and minimal-mass blow-up solutions for focusing NLS with Hardy potential ⋮ Instability of standing waves for the nonlinear Schrödinger-Poisson equation in the \(L^2\)-critical case ⋮ Existence of stable standing waves for the nonlinear Schrödinger equation with the Hardy potential

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