On asymptotic stability in energy space of ground states for nonlinear Schrödinger equations
From MaRDI portal
Publication:2517958
DOI10.1007/s00220-008-0605-3zbMath1155.35092arXiv0711.4195OpenAlexW2135269829MaRDI QIDQ2517958
Scipio Cuccagna, Tetsu Mizumachi
Publication date: 12 January 2009
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0711.4195
Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55)
Related Items (38)
Freezing of energy of a soliton in an external potential ⋮ On Stability of Standing Waves of Nonlinear Dirac Equations ⋮ Asymptotic stability for standing waves of a NLS equation with subcritical concentrated nonlinearity in dimension three: neutral modes ⋮ Attractors of Hamilton nonlinear PDEs ⋮ Gap eigenvalues and asymptotic dynamics of geometric wave equations on hyperbolic space ⋮ Klein–Gordon equation with mean field interaction. Orbital and asymptotic stability of solitary waves * ⋮ A critical center-stable manifold for Schrödinger's equation in three dimensions ⋮ Existence and Asymptotic Stability of Quasi-Periodic Solutions of Discrete NLS with Potential ⋮ Hylomorphic solitons ⋮ Attractors of nonlinear Hamiltonian partial differential equations ⋮ Global dynamics above the ground state energy for the cubic NLS equation in 3D ⋮ On scattering of small energy solutions of non-autonomous Hamiltonian nonlinear Schrödinger equations ⋮ Long Time Dynamics and Coherent States in Nonlinear Wave Equations ⋮ The Hamiltonian structure of the nonlinear Schrödinger equation and the asymptotic stability of its ground states ⋮ Small solutions of nonlinear Schrödinger equations near first excited states ⋮ New estimates for a time-dependent Schrödinger equation ⋮ Asymptotic stability of ground states in some Hamiltonian PDEs with symmetry ⋮ On asymptotic stability in energy space of ground states of NLS in 1D ⋮ Asymptotic stability of multi-soliton solutions for nonlinear Schrödinger equations with time-dependent potential ⋮ Orbital and asymptotic stability for standing waves of a nonlinear Schrödinger equation with concentrated nonlinearity in dimension three ⋮ Dispersive Properties of Schrödinger Operators in the Absence of a Resonance at Zero Energy in 3D ⋮ On asymptotic stability of ground states of NLS with a finite bands periodic potential in 1D ⋮ On asymptotic stability of moving ground states of the nonlinear Schrödinger equation ⋮ On eigenfunction expansion of solutions to the Hamilton equations ⋮ On asymptotic stability in energy space of ground states of NLS in 2D ⋮ On asymptotic stability of kink for relativistic Ginzburg-Landau equations ⋮ Asymptotic stability of solitons to 1D nonlinear Schrödinger equations in subcritical case ⋮ Soliton-Potential Interactions for Nonlinear Schrödinger Equation in $\mathbb{R}^3$ ⋮ Fermi's golden rule and \(H^1\) scattering for nonlinear Klein-Gordon equations with metastable states ⋮ On dispersion decay for 3D Klein-Gordon equation ⋮ On instability of excited states of the nonlinear Schrödinger equation ⋮ Decay of small odd solutions for long range Schrödinger and Hartree equations in one dimension ⋮ A survey on asymptotic stability of ground states of nonlinear Schrödinger equations. II ⋮ Scattering of solitons for coupled wave-particle equations ⋮ Existence and Stability of Schrödinger Solitons on Noncompact Manifolds ⋮ Spectral stability of small amplitude solitary waves of the Dirac equation with the Soler-type nonlinearity ⋮ Endpoint Strichartz estimates for charge transfer Hamiltonians ⋮ Asymptotic stability of small gap solitons in nonlinear Dirac equations
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Stability theory of solitary waves in the presence of symmetry. II
- Asymptotic stability of small solitons for 2D nonlinear Schrödinger equations with potential
- Orbital stability of standing waves for some nonlinear Schrödinger equations
- Instability of nonlinear bound states
- Stability theory of solitary waves in the presence of symmetry. I
- Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
- Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations
- Multichannel nonlinear scattering for nonintegrable equations. II: The case of anisotropic potentials and data
- Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations
- Classification of asymptotic profiles for nonlinear Schrödinger equations with small initial data
- Asymptotic dynamics of nonlinear Schrödinger equations with many bound states.
- Nonlinear wave and Schrödinger equations. I: Instability of periodic and quasiperiodic solutions
- On asymptotic stability of solitary waves for nonlinear Schrödinger equations
- Stability of solitary waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities
- On asymptotic stability in energy space of ground states of NLS in 2D
- Relaxation of solitons in nonlinear Schrödinger equations with potential
- A remark on linearly unstable standing wave solutions to NLS
- Uniqueness of Positive Radial Solutions of Δu + f(u) = 0 in ℝ n , II
- Spectra of positive and negative energies in the linearized NLS problem
- Asymptotic Stability of Multi-soliton Solutions for Nonlinear Schrödinger Equations
- Bifurcations from the endpoints of the essential spectrum in the linearized nonlinear Schrödinger problem
- Dispersion for Schrödinger Equation with Periodic Potential in 1D
- Modulational Stability of Ground States of Nonlinear Schrödinger Equations
- Lyapunov stability of ground states of nonlinear dispersive evolution equations
- Endpoint Strichartz estimates
- Uniqueness of positive radial solutions of semilinear elliptic equations in RNand séré's non—degeneracy condition
- A note on asymptotic uniqueness for some nonlinearities which change sign
- On a cubic-quintic Ginzburg-Landau equation with global coupling
- Stabilization of solutions to nonlinear Schrödinger equations
- Asymptotic dynamics of nonlinear Schrödinger equations: Resonance-dominated and dispersion-dominated solutions
- ON ASYMPTOTIC STABILITY OF GROUND STATES OF NLS
- SELECTION OF THE GROUND STATE FOR NONLINEAR SCHRÖDINGER EQUATIONS
- The \(W^{k,p}\)-continuity of wave operators for Schrödinger operators
- Modulational approach to stability of non-topological solitons in semilinear wave equations.
- Center manifold for nonintegrable nonlinear Schrödinger equations on the line
This page was built for publication: On asymptotic stability in energy space of ground states for nonlinear Schrödinger equations