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A survey on asymptotic stability of ground states of nonlinear Schrödinger equations. II (Q2057689)

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English	A survey on asymptotic stability of ground states of nonlinear Schrödinger equations. II	scientific article

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scholarly article

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A survey on asymptotic stability of ground states of nonlinear Schrödinger equations. II (English)

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Scipio Cuccagna

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Discrete and Continuous Dynamical Systems. Series S

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publication date

7 December 2021

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full work available at URL

https://arxiv.org/abs/2009.00573

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zbMATH Keywords

ground state

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stability

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dispersion

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normal form

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metastability

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MaRDI profile type

MaRDI publication profile

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Orbital and asymptotic stability for standing waves of a nonlinear Schrödinger equation with concentrated nonlinearity in dimension three

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Fermi's golden rule and \(H^1\) scattering for nonlinear Klein-Gordon equations with metastable states

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Embedded eigenvalues and the nonlinear Schrödinger equation

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Asymptotic stability of ground states in some Hamiltonian PDEs with symmetry

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On dispersion of small energy solutions of the nonlinear Klein Gordon equation with a potential

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Freezing of energy of a soliton in an external potential

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Exact solitary water waves with capillary ripples at infinity

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New estimates for a time-dependent Schrödinger equation

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Dissipation induced instabilities

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Long time dynamics of highly concentrated solitary waves for the nonlinear Schrödinger equation

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Long time asymptotic behavior of the focusing nonlinear Schrödinger equation

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On Stability of Standing Waves of Nonlinear Dirac Equations

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Simulation of instability of bright solitons for NLS with saturating nonlinearity

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On Asymptotic Stability of Solitary Waves in Schrödinger Equation Coupled to Nonlinear Oscillator

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On asymptotic stability of solitary waves for nonlinear Schrödinger equations

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Spectra of Linearized Operators for NLS Solitary Waves

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Solutions with compact time spectrum to nonlinear Klein-Gordon and Schrödinger equations and the Titchmarsh theorem for partial convolution

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On asymptotic stability of ground states of some systems of nonlinear Schrödinger equations

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Purely nonlinear instability of standing waves with minimal energy

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On the spectral properties of<i>L</i><sub>±</sub>in three dimensions

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The Hamiltonian structure of the nonlinear Schrödinger equation and the asymptotic stability of its ground states

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On asymptotic stability of moving ground states of the nonlinear Schrödinger equation

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Stabilization of solutions to nonlinear Schrödinger equations

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ON ASYMPTOTIC STABILITY OF GROUND STATES OF NLS

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On weak interaction between a ground state and a non-trapping potential

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On small energy stabilization in the NLS with a trapping potential

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On weak interaction between a ground state and a trapping potential

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On orbital instability of spectrally stable vortices of the NLS in the plane

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On Nonlinear Profile Decompositions and Scattering for an NLS–ODE Model

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Long time oscillation of solutions of nonlinear Schrödinger equations near minimal mass ground state

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On Stability of Small Solitons of the 1-D NLS with a Trapping Delta Potential

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On small energy stabilization in the NLKG with a trapping potential

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On asymptotic stability in energy space of ground states for nonlinear Schrödinger equations

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The asymptotic stability of solitons in the cubic NLS equation on the line

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Spectra of positive and negative energies in the linearized NLS problem

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On stabilization of small solutions in the nonlinear Dirac equation with a trapping potential

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On asymptotic stability in energy space of ground states of NLS in 2D

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On Asymptotic Stability of Standing Waves of Discrete Schrödinger Equation in $\mathbb{Z}$

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Fast Soliton Scattering by Attractive Delta Impurities

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Orbital Stability: Analysis Meets Geometry

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Perturbation theory for infinite-dimensional integrable systems on the line. A case study

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Numerical verification of a gap condition for a linearized nonlinear Schrödinger equation

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Soliton-Potential Interactions for Nonlinear Schrödinger Equation in $\mathbb{R}^3$

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Classification of the radial solutions of the focusing, energy-critical wave equation

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Solitary wave dynamics in an external potential

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Perturbation expansion and Nth order Fermi golden rule of the nonlinear Schrödinger equations

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Relaxation of solitons in nonlinear Schrödinger equations with potential

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ASYMPTOTIC STABILITY OF NONLINEAR SCHRÖDINGER EQUATIONS WITH POTENTIAL

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Dynamics of nonlinear Schrödinger/Gross-Pitaevskii equations: mass transfer in systems with solitons and degenerate neutral modes

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Equipartition of Mass in Nonlinear Schrödinger/Gross–Pitaevskii Equations

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Self-trapping and Josephson tunneling solutions to the nonlinear Schrödinger / Gross-Pitaevskii equation

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Analysis of the linearization around a critical point of an infinite dimensional hamiltonian system

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Stable Directions for Degenerate Excited States of Nonlinear Schrödinger Equations

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Radiation Induced Instability

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Nanopteron solutions of diatomic Fermi-Pasta-Ulam-Tsingou lattices with small mass-ratio

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Soliton splitting by external delta potentials

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Fast soliton scattering by delta impurities

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Soliton Interaction with Slowly Varying Potentials

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Slow solution interaction with delta imperiums

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On the Weinstein-Aronszajn formula

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Puiseux series for resonances at an imbedded eigenvalue

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Long time motion of NLS solitary waves in a confining potential

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On an elliptic equation related to the blow-up phenomenon in the nonlinear Schrödinger equation

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Generalized solitary waves in the gravity‐capillary Whitham equation

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Decay estimates for Schrödinger operators

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Wave operators and similarity for some non-selfadjoint operators

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Endpoint Strichartz estimates

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Symmetry-breaking bifurcation in the nonlinear Schrödinger equation with symmetric potentials

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Symmetry-Breaking Bifurcation in Nonlinear Schrödinger/Gross–Pitaevskii Equations

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Asymptotic stability of ground states in 3D nonlinear Schrödinger equation including subcritical cases

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Asymptotic stability of ground states in 2D nonlinear Schrödinger equation including subcritical cases

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Global attraction to solitary waves for Klein-Gordon equation with mean field interaction

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Global Attraction to Solitary Waves for a Nonlinear Dirac Equation with Mean Field Interaction

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On global attraction to solitary waves for the Klein-Gordon field coupled to several nonlinear oscillators

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On asymptotic stability of solitons in a nonlinear Schrödinger equation

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Kink dynamics in the $\phi ^4$ model: Asymptotic stability for odd perturbations in the energy space

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Soliton dynamics for the 1D NLKG equation with symmetry and in the absence of internal modes

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Stable manifolds for all monic supercritical focusing nonlinear Schrödinger equations in one dimension

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Nanoptera and Stokes curves in the 2-periodic Fermi-Pasta-Ulam-Tsingou equation

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Nanoptera in a Period-2 Toda Chain

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Asymptotic stability of solitons of the gKdV equations with general nonlinearity

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A system of ODEs for a perturbation of a minimal mass soliton

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Spectral analysis for matrix Hamiltonian operators

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Long time dynamics near the symmetry breaking bifurcation for nonlinear Schrödinger/Gross-Pitaevskii equations

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Stability of small solitary waves for the one-dimensional NLS with an attractive delta potential

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Modified Scattering for the One-Dimensional Cubic NLS with a Repulsive Delta Potential

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On a sharp lower bound on the blow-up rate for the 𝐿² critical nonlinear Schrödinger equation

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Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation

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The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation

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Asymptotic stability of small solitary waves to 1D nonlinear Schrödinger equations with potential

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Asymptotic stability of small solitons for 2D nonlinear Schrödinger equations with potential

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On the solitary wave dynamics, under slowly varying medium, for nonlinear Schrödinger equations

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Global dynamics below excited solitons for the nonlinear Schrödinger equation with a potential

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Small solutions of nonlinear Schrödinger equations near first excited states

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On traveling waves of the nonlinear Schrödinger equation escaping a potential well

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Internal modes of envelope solitons

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Two soliton collision for nonlinear Schrödinger equations in dimension 1

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A remark on soliton-potential interactions for nonlinear Schrödinger equations

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Asymptotic Stability of Multi-soliton Solutions for Nonlinear Schrödinger Equations

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On the formation of singularities in solutions of the critical nonlinear Schrödinger equation

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Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations

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Dispersive analysis of charge transfer models

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Asymptotic stability of N-solitons in the cubic NLS equation

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Stable manifolds for an orbitally unstable nonlinear Schrödinger equation

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Nonlinear wave and Schrödinger equations. I: Instability of periodic and quasiperiodic solutions

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Multichannel nonlinear scattering for nonintegrable equations

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Multichannel nonlinear scattering for nonintegrable equations. II: The case of anisotropic potentials and data

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Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations

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SELECTION OF THE GROUND STATE FOR NONLINEAR SCHRÖDINGER EQUATIONS

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Lectures on the orbital stability of standing waves and application to the nonlinear Schrödinger equation

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The focusing nonlinear Schrödinger equation: Effect of the coupling to a low frequency field

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Existence of a generalized solitary wave solution for water with positive Bond number less than 1/3

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Asymptotic dynamics of nonlinear Schrödinger equations with many bound states.

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Asymptotic dynamics of nonlinear Schrödinger equations: Resonance-dominated and dispersion-dominated solutions

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Classification of asymptotic profiles for nonlinear Schrödinger equations with small initial data

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STABLE DIRECTIONS FOR EXCITED STATES OF NONLINEAR SCHRÖDINGER EQUATIONS

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The \(W_{k,p}\)-continuity of the Schrödinger wave operators on the line

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\(L^p\)-\(L^{\acute p}\) estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential

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Modulational Stability of Ground States of Nonlinear Schrödinger Equations

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The \(W^{k,p}\)-continuity of wave operators for Schrödinger operators

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.3934/DCDSS.2020450

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Sitelinks

Mathematics(1 entry)

mardi Publication:2057689

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