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On asymptotic stability of nonlinear waves (Q2053920)

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scientific article; zbMATH DE number 7436118

Language	Label	Description	Also known as
English	On asymptotic stability of nonlinear waves	scientific article; zbMATH DE number 7436118

Statements

scholarly article

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On asymptotic stability of nonlinear waves (English)

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Michal Kowalczyk

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Séminaire Laurent Schwartz. EDP et Applications

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publication date

30 November 2021

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MaRDI profile type

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full work available at URL

https://doi.org/10.5802/slsedp.111

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The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems

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Nonlinear stability of MKdV breathers

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Almost sharp nonlinear scattering in one-dimensional Born-Infeld equations arising in nonlinear electrodynamics

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Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire

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Asymptotic stability in energy space for dark solitons of the Landau-Lifshitz equation

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

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A centre-stable manifold for the focussing cubic NLS in \({\mathbb{R}}^{1+3\star}\)

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A critical center-stable manifold for Schrödinger's equation in three dimensions

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Asymptotic stability of the Toda \(m\)-soliton

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Model equations for long waves in nonlinear dispersive systems

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Nonlinear scalar field equations. I: Existence of a ground state

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Asymptotic stability in the energy space for dark solitons of the Gross-Pitaevskii equation

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Dynamics near the threshold for blowup in the one-dimensional focusing nonlinear Klein-Gordon equation

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On the stability theory of solitary waves

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Stability and instability of solitary waves of Korteweg-de Vries type

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Long time asymptotic behavior of the focusing nonlinear Schrödinger equation

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The Korteweg-de Vries equation at \(H^{-1}\) regularity

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On asymptotic stability of solitary waves for nonlinear Schrödinger equations

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Orbital stability of standing waves for some nonlinear Schrödinger equations

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Spectra of Linearized Operators for NLS Solitary Waves

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Uniqueness of the ground state solution for \(\Delta u - u + u^3=0\) and a variational characterization of other solutions

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Existence and regularity for solutions of the Korteweg-de Vries equation

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A degenerate edge bifurcation in the 1D linearized nonlinear Schrödinger equation

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Construction and characterization of solutions converging to solitons for supercritical gKdV equations.

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Multi-Soliton Solutions for the Supercritical gKdV Equations

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Multi-existence of multi-solitons for the supercritical nonlinear Schrödinger equation in one dimension

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Stability of multi-solitons in the cubic NLS equation

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

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On the Soliton Resolution for Equivariant Wave Maps to the Sphere

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Asymptotic stability of high-dimensional Zakharov-Kuznetsov solitons

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Solitary water wave interactions

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ON ASYMPTOTIC STABILITY OF GROUND STATES OF NLS

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On asymptotic stability in 3D of kinks for the 𝜙⁴ model

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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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On the asymptotic stability of \(N\)-soliton solutions of the defocusing nonlinear Schrödinger equation

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

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Sine-Gordon wobbles through Bäcklund transformations

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Construction of a multisoliton blowup solution to the semilinear wave equation in one space dimension

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Inverse scattering on the line

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The collisionless shock region for the long‐time behavior of solutions of the KdV equation

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Global existence and asymptotics for the quasilinear Klein-Gordon equation with small data in one space dimension

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Semiclassical microlocal normal forms and global solutions of modified one-dimensional KG equations

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Global existence of small solutions for quadratic quasilinear Klein-Gordon systems in two space dimensions

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Nonpersistence of breather families for the perturbed sine Gordon equation

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Dynamics of Threshold Solutions for Energy-Critical Wave Equation

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Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation

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Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case

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

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Solutions of the focusing nonradial critical wave equation with the compactness property

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Soliton resolution along a sequence of times for the focusing energy critical wave equation

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The emergence of solitons of the korteweg-de vries equation from arbitrary initial conditions

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Asymptotic stability of solitary waves for the Benjamin-Bona-Mahony equation

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Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman

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Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\)

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Method for Solving the Korteweg-deVries Equation

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A two-soliton with transient turbulent regime for the cubic half-wave equation on the real line

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Asymptotic stability of solitons for mKdV

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Limits of soliton solutions

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Symmetry and related properties via the maximum principle

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On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case

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Dispersive estimates for Schrödinger operators in dimensions one and three

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Asymptotic stability of the black soliton for the Gross–Pitaevskii equation

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Linearized instability for nonlinear schrödinger and klein-gordon equations

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Stability theory of solitary waves in the presence of symmetry. I

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Asymptotic stability, concentration, and oscillation in harmonic map heat-flow, Landau-Lifshitz, and Schrödinger maps on \(\mathbb R^2\)

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The initial value problem for the cubic nonlinear Klein-Gordon equation

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Quadratic nonlinear Klein-Gordon equation in one dimension

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Stability theory for solitary-wave solutions of scalar field equations

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Asymptotic two-soliton solutions in the Fermi-Pasta-Ulam model

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A Simple Proof of the Stability of Solitary Waves in the Fermi-Pasta-Ulam Model Near the KdV Limit

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Orbital stability of localized structures via Bäcklund transformations.

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Construction of type II blow-up solutions for the energy-critical wave equation in dimension 5

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Nonexistence of two-bubbles with opposite signs for the radial energy-critical wave equation

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Focusing nonlinear Schrödinger equation with infinitely many solitons

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Stable soliton resolution for exterior wave maps in all equivariance classes

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Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation

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Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle

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Global existence for nonlinear wave equations

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Global existence of small amplitude solutions to nonlinear klein-gordon equations in four space-time dimensions

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Small data scattering and soliton stability in \(\dot{H}^{-1/6}\) for the quartic KdV equation

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On asymptotic stability of kink for relativistic Ginzburg-Landau equations

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On asymptotic stability of moving kink for relativistic Ginzburg-Landau 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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Nonexistence of small, odd breathers for a class of nonlinear wave equations

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Global dynamics above the ground state energy for the one-dimensional NLKG equation

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Global dynamics away from the ground state for the energy-critical nonlinear wave equation

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Global dynamics of the nonradial energy-critical wave equation above the ground state energy

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

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Slow blow-up solutions for the \(H^1(\mathbb R^3)\) critical focusing semilinear wave equation

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Integrals of nonlinear equations of evolution and solitary waves

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Nondegeneracy, Morse index and orbital stability of the KP-I lump solution

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A REMARK ON LONG RANGE SCATTERING FOR THE NONLINEAR KLEIN–GORDON EQUATION

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A remark on asymptotic completeness for the critical nonlinear Klein-Gordon equation

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Scattering for the Klein-Gordon equation with quadratic and variable coefficient cubic nonlinearities

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On the stability of KdV multi‐solitons

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Topological Solitons

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Asymptotic N -soliton-like solutions of the subcritical and critical generalized Korteweg-de Vries equations

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Instability of solitons for the critical generalized Korteweg-de Vries equation

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A Liouville theorem for the critical generalized Korteweg-de Vries equation

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Asymptotic stability of solitons for subcritical generalized KdV equations

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Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation

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Asymptotic stability of solitons of the subcritical gKdV equations revisited

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Stability and asymptotic stability for subcritical gKdV equations

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Stability in \(H^1\) of the sum of \(K\) solitary waves for some nonlinear Schrödinger equations

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Existence of blow-up solutions in the energy space for the critical generalized KdV 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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On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation

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Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation

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On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations

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Multi-solitons and Related Solutions for the Water-waves System

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The Korteweg–deVries Equation: A Survey of Results

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Large time asymptotics of solutions around solitary waves to the generalized Korteweg-de Vries equations

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Asymptotic stability of solitary wave solutions to the regularized long-wave equation

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Stability of line solitons for the KP-II equation in ℝ²

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Stability of line solitons for the KP-II equation in ℝ<sup>2</sup>. II

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Asymptotic stability of Toda lattice solitons

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Scattering in the energy space for Boussinesq equations

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Invariant manifolds and dispersive Hamiltonian evolution equations

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Blow-Up of H 1 Solutions for the One-Dimensional Nonlinear Schrodinger Equations with Critical Power Nonlinearity

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Asymptotic linear stability of solitary water waves

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On the transverse linear instability of solitary water waves with large surface tension

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Eigenvalues, and instabilities of solitary waves

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Asymptotic stability of solitary waves

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Dispersive analysis of charge transfer models

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Transverse nonlinear instability of solitary waves for some Hamiltonian PDE's

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Transverse instability of the line solitary water-waves

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Spectral theory and nonlinear partial differential equations: a survey

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Stable manifolds for an orbitally unstable nonlinear Schrödinger equation

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Asymptotic analysis of soliton problems. An inverse scattering approach

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Normal forms and quadratic nonlinear Klein-Gordon equations

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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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Time dependent resonance theory

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Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations

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Dispersive decay for the 1D Klein-Gordon equation with variable coefficient nonlinearities

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Best constant in Sobolev inequality

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Scattering for the quartic generalised Korteweg-de Vries equation

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Why are solitons stable?

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

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Long-time asymptotics of solutions to the Cauchy problem for the defocusing nonlinear Schrödinger equation with finite-density initial data. II: Dark solitons on continua

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Nonexistence of spatially localized free vibrations for a class of nonlinear wave 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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Nonlinear Schrödinger equations and sharp interpolation estimates

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Modulational Stability of Ground States of Nonlinear Schrödinger Equations

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Lyapunov stability of ground states of nonlinear dispersive evolution equations

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From superconductors and four-manifolds to weak interactions

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Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States

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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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10.5802/SLSEDP.111

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Sitelinks

Mathematics(1 entry)

mardi Publication:2053920

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