On instability of excited states of the nonlinear Schrödinger equation
type: Item
instance of: scholarly article
title: On instability of excited states of the nonlinear Schrödinger equation
zbMATH Open document ID: 1161.35500
author: Scipio Cuccagna
published in: Physica D
publication date: 2009-02-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/0801.4237
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 37K45
zbMATH DE Number: 5506313
zbMATH Keywords: stability
zbMATH Keywords: standing wave
zbMATH Keywords: nonlinear Schrödinger equation
MaRDI profile type: Publication
OpenAlex ID: W2593568386
arXiv ID: 0801.4237
cites work: Orbital stability of standing waves for some nonlinear Schrödinger equations
cites work: Lyapunov stability of ground states of nonlinear dispersive evolution equations
cites work: Stability theory of solitary waves in the presence of symmetry. I
cites work: Stability theory of solitary waves in the presence of symmetry. II
cites work: Purely nonlinear instability of standing waves with minimal energy
cites work: A remark on linearly unstable standing wave solutions to NLS
cites work: An instability mechanism for radially symmetric standing waves of a nonlinear Schrödinger equation
cites work: Analysis of the linearization around a critical point of an infinite dimensional hamiltonian system
cites work: Linearized instability for nonlinear schrödinger and klein-gordon equations
cites work: Vortex solitons for 2D focusing nonlinear Schrödinger equation.
cites work: Instability of bound states for 2D nonlinear Schrö\-dinger equations
cites work: Instability of vortex solitons for 2D focusing NLS
cites work: On asymptotic stability in energy space of ground states for nonlinear Schrödinger equations
cites work: STABLE DIRECTIONS FOR EXCITED STATES OF NONLINEAR SCHRÖDINGER EQUATIONS
cites work: Spectra of positive and negative energies in the linearized NLS problem
cites work: Q4853576
cites work: Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations
cites work: Asymptotic dynamics of nonlinear Schrödinger equations: Resonance-dominated and dispersion-dominated solutions
cites work: Q3147641
cites work: Classification of asymptotic profiles for nonlinear Schrödinger equations with small initial data
cites work: ON ASYMPTOTIC STABILITY OF GROUND STATES OF NLS
cites work: On asymptotic stability of solitary waves for nonlinear Schrödinger equations
cites work: Asymptotic dynamics of nonlinear Schrödinger equations with many bound states.
cites work: SELECTION OF THE GROUND STATE FOR NONLINEAR SCHRÖDINGER EQUATIONS
cites work: On asymptotic stability in energy space of ground states of NLS in 1D
cites work: On asymptotic stability in energy space of ground states of NLS in 2D
cites work: Nonlinear wave and Schrödinger equations. I: Instability of periodic and quasiperiodic solutions
cites work: Perturbation expansion and Nth order Fermi golden rule of the nonlinear Schrödinger equations
cites work: Q5653193
cites work: Perturbation of embedded eigenvalues in the generalized N-body problem
cites work: Perturbations of the Wigner-von Neumann potential leaving the embedded eigenvalue fixed
cites work: Modulational Stability of Ground States of Nonlinear Schrödinger Equations
cites work: Spectral properties of Schrödinger operators and time-decay of the wave functions
cites work: Dynamics of nonlinear Schrödinger/Gross-Pitaevskii equations: mass transfer in systems with solitons and degenerate neutral modes
cites work: Stabilization of solutions to nonlinear Schrödinger equations
cites work: Bifurcations from the endpoints of the essential spectrum in the linearized nonlinear Schrödinger problem
DOI: 10.1016/J.PHYSD.2008.08.010
description: scientific article