Existence and Stability of Schrödinger Solitons on Noncompact Manifolds

DOI10.1137/18M1216031zbMath1428.35486arXiv1809.07643OpenAlexW2975227509MaRDI QIDQ5234597

Roland Donninger, Jeremy L. Marzuola, Enno Lenzmann, David Borthwick

Publication date: 27 September 2019

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.07643

zbMATH Keywords

stabilitynonlinear Schrödinger equationsoliton

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55) Perturbations in context of PDEs (35B20) Blow-up in context of PDEs (35B44) Soliton solutions (35C08)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dispersive estimates for scalar and matrix Schrödinger operators on \(\mathbb H^{n+1}\)
• The Hamiltonian structure of the nonlinear Schrödinger equation and the asymptotic stability of its ground states
• Symmetry-breaking bifurcation in the nonlinear Schrödinger equation with symmetric potentials
• Nonlinear Schrödinger equation on real hyperbolic spaces
• Nonlinear Schrödinger equations and sharp interpolation estimates
• Nonlinear scalar field equations. I: Existence of a ground state
• Stability theory of solitary waves in the presence of symmetry. II
• A centre-stable manifold for the focussing cubic NLS in \({\mathbb{R}}^{1+3\star}\)
• Strichartz estimates and local smoothing estimates for asymptotically flat Schrödinger equations
• 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 radial solutions of \(\Delta u+f(u)=0\) in \({\mathbb{R}}^ n\)
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Multichannel nonlinear scattering for nonintegrable equations. II: The case of anisotropic potentials and data
• Existence of solitary waves in higher dimensions
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations
• Global dynamics below excited solitons for the nonlinear Schrödinger equation with a potential
• Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds. III: Global-in-time Strichartz estimates without loss
• Perturbation theory for linear operators.
• On asymptotic stability of solitary waves for nonlinear Schrödinger equations
• Global existence, scattering and blow-up for the focusing NLS on the hyperbolic space
• Global dynamics above the first excited energy for the nonlinear Schrödinger equation with a potential
• Stable manifolds for an orbitally unstable nonlinear Schrödinger equation
• Global dynamics above the ground state energy for the cubic NLS equation in 3D
• Weighted Strichartz estimates for radial Schrödinger equation on noncompact manifolds
• The nonlinear Schrödinger equation ground states on product spaces
• On asymptotic stability in energy space of ground states for nonlinear Schrödinger equations
• On the essential spectrum
• Uniqueness of the ground state solution for \(\Delta u - u + u^3=0\) and a variational characterization of other solutions
• Global-in-time Strichartz estimates on nontrapping, asymptotically conic manifolds
• Multichannel nonlinear scattering for nonintegrable equations
• Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds I: Resolvent construction at high energy
• Nonlinear Bound States in a Schrödinger--Poisson System with External Potential
• Spectral analysis for matrix Hamiltonian operators
• Low Frequency Estimates and Local Energy Decay for Asymptotically Euclidean Laplacians
• On the spectral properties ofL_±in three dimensions
• Spectra of positive and negative energies in the linearized NLS problem
• Asymptotic Stability of Multi-soliton Solutions for Nonlinear Schrödinger Equations
• A critical center-stable manifold for Schrödinger's equation in three dimensions
• Decay for the wave and Schrödinger evolutions on manifolds with conical ends, Part I
• Riemannian Geometry
• Spectra of Linearized Operators for NLS Solitary Waves
• Symmetry-Breaking Bifurcation in Nonlinear Schrödinger/Gross–Pitaevskii Equations
• Modulational Stability of Ground States of Nonlinear Schrödinger Equations
• Lyapunov stability of ground states of nonlinear dispersive evolution equations
• Linearized instability for nonlinear schrödinger and klein-gordon equations
• Existence d'une infinité d'ondes solitaires pour des équations de champs non linéaires dans le plan
• 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
• Quantum Mechanics
• Nonlinear Bound States on Weakly Homogeneous Spaces
• Exponential decay of eigenfunctions and generalized eigenfunctions of a non-self-adjoint matrix Schrödinger operator related to NLS
• The Nonlinear Schrödinger Equation on Hyperbolic Space
• Stable manifolds for all monic supercritical focusing nonlinear Schrödinger equations in one dimension
• Numerical verification of a gap condition for a linearized nonlinear Schrödinger equation
• Existence and stability of solitons for the nonlinear Schrödinger equation on hyperbolic space
• Operator Theory

This page was built for publication: Existence and Stability of Schrödinger Solitons on Noncompact Manifolds