Asymptotic stability of multi-soliton solutions for nonlinear Schrödinger equations with time-dependent potential
From MaRDI portal
Publication:3298899
DOI10.1063/1.5144330zbMath1443.81029OpenAlexW3016826025MaRDI QIDQ3298899
Publication date: 16 July 2020
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.5144330
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Linearizations (93B18) NLS equations (nonlinear Schrödinger equations) (35Q55) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41) Sobolev (and similar kinds of) spaces of functions of discrete variables (46E39)
Related Items
Cites Work
- On the asymptotic stability of \(N\)-soliton solutions of the defocusing nonlinear Schrödinger equation
- On the solitary wave dynamics, under slowly varying medium, for nonlinear Schrödinger equations
- On small energy stabilization in the NLS with a trapping potential
- Strichartz estimates for charge transfer models
- Two soliton collision for nonlinear Schrödinger equations in dimension 1
- Adiabatic theorems and applications to the quantum Hall effect
- New estimates for a time-dependent Schrödinger equation
- Geometric methods in scattering theory of the charge transfer model
- On soliton dynamics in nonlinear Schrödinger equations
- Multi solitary waves for nonlinear Schrödinger equations
- Stability theory of solitary waves in the presence of symmetry. II
- Asymptotic stability of small solitons for 2D nonlinear Schrödinger equations with potential
- Asymptotic stability of small solitary waves to 1D nonlinear Schrödinger equations with potential
- Colliding solitons for the nonlinear Schrödinger equation
- 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
- A multi-channel scattering theory for some time dependent Hamiltonians, charge transfer problem
- Multichannel nonlinear scattering for nonintegrable equations. II: The case of anisotropic potentials and data
- Existence of solitary waves in higher dimensions
- Nonlinear scattering: The states which are close to a soliton
- Asymptotic completeness for multiparticle dispersive charge transfer models
- Classification of asymptotic profiles for nonlinear Schrödinger equations with small initial data
- Asymptotic dynamics of nonlinear Schrödinger equations with many bound states.
- Global dynamics below excited solitons for the nonlinear Schrödinger equation with a potential
- On the 4D nonlinear Schrödinger equation with combined terms under the energy threshold
- Existence of multi-solitary waves with logarithmic relative distances for the NLS equation
- On asymptotic stability of solitary waves for nonlinear Schrödinger equations
- On asymptotic stability in energy space of ground states of NLS in 2D
- High-speed excited multi-solitons in nonlinear Schrödinger equations
- Stable manifolds for an orbitally unstable nonlinear Schrödinger equation
- On weak interaction between a ground state and a non-trapping potential
- Relaxation of solitons in nonlinear Schrödinger equations with potential
- Stability in \(H^1\) of the sum of \(K\) solitary waves for some nonlinear Schrödinger equations
- On asymptotic stability in energy space of ground states for nonlinear Schrödinger equations
- Uniqueness of the ground state solution for \(\Delta u - u + u^3=0\) and a variational characterization of other solutions
- Multichannel nonlinear scattering for nonintegrable equations
- Orbital Stability: Analysis Meets Geometry
- Resonant Tunneling of Fast Solitons through Large Potential Barriers
- Endpoint Strichartz estimates for charge transfer Hamiltonians
- Spectra of positive and negative energies in the linearized NLS problem
- Asymptotic Stability of Multi-soliton Solutions for Nonlinear Schrödinger Equations
- ASYMPTOTIC STABILITY OF NONLINEAR SCHRÖDINGER EQUATIONS WITH POTENTIAL
- Solitary wave dynamics in time-dependent potentials
- Modulational Stability of Ground States of Nonlinear Schrödinger Equations
- Lyapunov stability of ground states of nonlinear dispersive evolution equations
- Decay estimates for Schrödinger operators
- Endpoint Strichartz estimates
- Purely nonlinear instability of standing waves with minimal energy
- Stability of multisolitons for the derivative nonlinear Schrödinger equation
- Dispersive analysis of charge transfer models
- Soliton-Potential Interactions for Nonlinear Schrödinger Equation in $\mathbb{R}^3$
- Stabilization of solutions to nonlinear Schrödinger equations
- Asymptotic dynamics of nonlinear Schrödinger equations: Resonance-dominated and dispersion-dominated solutions
- STABLE DIRECTIONS FOR EXCITED STATES OF NONLINEAR SCHRÖDINGER EQUATIONS
- ON ASYMPTOTIC STABILITY OF GROUND STATES OF NLS
- On asymptotic stability of moving ground states of the nonlinear Schrödinger equation
- SELECTION OF THE GROUND STATE FOR NONLINEAR SCHRÖDINGER EQUATIONS
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
