Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations

DOI10.2969/jmsj/06420533zbMath1253.35158arXiv1009.5184OpenAlexW2109682907MaRDI QIDQ431611

Vladimir Georgiev, Masahito Ohta

Publication date: 29 June 2012

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.5184

zbMATH Keywords

instabilitynonlinear Schrödinger equationStrichartz estimatestanding wave

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (15)

Stability of traveling waves of nonlinear Schrödinger equation with nonzero condition at infinity ⋮ Integrability and linear stability of nonlinear waves ⋮ Plane wave stability analysis of Hartree and quantum dissipative systems ⋮ Transverse instability for a system of nonlinear Schrödinger equations ⋮ On the standing waves of the NLS-log equation with a point interaction on a star graph ⋮ On orbital instability of spectrally stable vortices of the NLS in the plane ⋮ Instability of bound states for abstract nonlinear Schrödinger equations ⋮ On the Cauchy Problem and the Black Solitons of a Singularly Perturbed Gross--Pitaevskii Equation ⋮ On spectral stability of the nonlinear Dirac equation ⋮ Linear instability and nondegeneracy of ground state for combined power-type nonlinear scalar field equations with the Sobolev critical exponent and large frequency parameter ⋮ On linear instability of solitary waves for the nonlinear Dirac equation ⋮ Transverse stability of line soliton and characterization of ground state for wave guide Schrödinger equations ⋮ Nonlinear dispersive equations: classical and new frameworks ⋮ Spectral stability of small amplitude solitary waves of the Dirac equation with the Soler-type nonlinearity ⋮ Stability properties of standing waves for NLS equations with the \(\delta^\prime\)-interaction

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear scalar field equations. II: Existence of infinitely many solutions
• Nonlinear Schrödinger equations and sharp interpolation estimates
• Stability of semiclassical bound states of nonlinear Schrödinger equations with potentials
• Scattering theory in the energy space for a class of nonlinear wave equations
• Stability theory of solitary waves in the presence of symmetry. II
• Instability of vortex solitons for 2D focusing NLS
• On instability of excited states of the nonlinear Schrödinger equation
• Stability of solitary waves for a system of nonlinear Schrödinger equations with three wave interaction
• Orbital stability of standing waves for some nonlinear Schrödinger equations
• Instability of nonlinear bound states
• An instability mechanism for radially symmetric standing waves of a nonlinear Schrödinger equation
• Stability theory of solitary waves in the presence of symmetry. I
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Existence of solitary waves in higher dimensions
• Nonradial solutions of a semilinear elliptic equation in two dimensions
• A remark on linearly unstable standing wave solutions to NLS
• Instability of bound states for 2D nonlinear Schrö\-dinger equations
• Instability of bound states of nonlinear Schrödinger equations with Morse index equal to two
• Spectra of positive and negative energies in the linearized NLS problem
• Analysis of the linearization around a critical point of an infinite dimensional hamiltonian system
• Spectra of Linearized Operators for NLS Solitary Waves
• Instability of Standing Waves for a System of Nonlinear Schroedinger Equations with Three-Wave Interaction
• On the Spectrum of C 0 -Semigroups
• Modulational Stability of Ground States of Nonlinear Schrödinger Equations
• Linearized instability for nonlinear schrödinger and klein-gordon equations
• Global strong solutions for nonlinear Schrödinger equations
• Spectral Theory for Contraction Semigroups on Hilbert Space
• A spectral mapping theorem and invariant manifolds for nonlinear Schrodinger equations
• Instability of Stationary Bubbles
• The black solitons of one-dimensional NLS equations

This page was built for publication: Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations