Soliton dynamics for the nonlinear Schrödinger equation with magnetic field
From MaRDI portal
Publication:1041160
DOI10.1007/s00229-009-0307-yzbMath1179.81066arXiv0811.2584OpenAlexW2022321587MaRDI QIDQ1041160
Publication date: 30 November 2009
Published in: Manuscripta Mathematica (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0811.2584
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) PDEs in connection with quantum mechanics (35Q40) Soliton equations (35Q51) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)
Related Items
Ground states for fractional magnetic operators ⋮ The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with a magnetic field ⋮ Multiple complex-valued solutions for the nonlinear Schrödinger equations involving magnetic potentials ⋮ Fractional NLS equations with magnetic field, critical frequency and critical growth ⋮ Some characterizations of magnetic Sobolev spaces ⋮ Existence and multiplicity of solutions for nonlinear Schrödinger equations with magnetic field and Hartree type nonlinearities ⋮ On concentration of least energy solutions for magnetic critical Choquard equations ⋮ Nonlocal Schrödinger-Kirchhoff equations with external magnetic field ⋮ Soliton dynamics for a general class of Schrödinger equations ⋮ On the dynamics of solitons in the nonlinear Schrödinger equation ⋮ Multiple semiclassical solutions for a nonlinear Choquard equation with magnetic field ⋮ Modulational stability of ground states to nonlinear Kirchhoff equations ⋮ Semiclassical stationary states for nonlinear Schrödinger equations under a strong external magnetic field
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Perturbation methods and semilinear elliptic problems on \(\mathbb R^n\)
- WKB analysis for nonlinear Schrödinger equations with potential
- The Cauchy problem for the nonlinear Schrödinger equation in \(H^ 1\)
- The concentration-compactness principle in the calculus of variations. The locally compact case. II
- Stability theory of solitary waves in the presence of symmetry. II
- On multi-bump semi-classical bound states of nonlinear Schrödinger equations with electromagnetic fields
- Asymptotic evolution for the semiclassical nonlinear Schrödinger equation in presence of electric and magnetic fields
- Orbital stability of standing waves for some nonlinear Schrödinger equations
- Stability theory of solitary waves in the presence of symmetry. I
- Schrödinger operators with magnetic fields. III: Atoms in homogeneous magnetic field
- Schrödinger evolution equations with magnetic fields
- Multichannel nonlinear scattering for nonintegrable equations. II: The case of anisotropic potentials and data
- Schrödinger operators with magnetic fields. I: General interactions
- Separation of center of mass in homogeneous magnetic fields
- The nonlinear Schrödinger equation. Self-focusing and wave collapse
- On the point-particle (Newtonian) limit of the nonlinear Hartree equation
- Soliton dynamics in a potential
- Existence and semi-classical limit of the least energy solution to a nonlinear Schrödinger equation with electromagnetic fields
- Local well-posedness and smoothing effects of strong solutions for nonlinear Schrödinger equations with potentials and magnetic fields
- On asymptotic stability of solitary waves for nonlinear Schrödinger equations
- Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
- Semiclassical limit for nonlinear Schrödinger equations with electromagnetic fields
- Semiclassical stationary states of nonlinear Schrödinger equations with an external magnetic field.
- A semilinear Schrödinger equation in the presence of a magnetic field
- On the Schrödinger equation involving a critical Sobolev exponent and magnetic field
- Slow solution interaction with delta imperiums
- Long time motion of NLS solitary waves in a confining potential
- Solitary wave dynamics in an external potential
- Effective dynamics of magnetic vortices
- Multichannel nonlinear scattering for nonintegrable equations
- ON THE LOCATION OF SPIKES FOR THE SCHRÖDINGER EQUATION WITH ELECTROMAGNETIC FIELD
- Soliton Interaction with Slowly Varying Potentials
- Strichartz and Smoothing Estimates for Dispersive Equations with Magnetic Potentials
- Remarks on Non-Linear Schrödinger Equation with Magnetic Fields
- 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
- Nonlinear Schrödinger Equations with Repulsive Harmonic Potential and Applications
- SEMICLASSICAL LIMIT OF A CLASS OF SCHRÖDINGER EQUATIONS WITH POTENTIAL
- Dispersive analysis of charge transfer models
- Asymptotic dynamics of nonlinear Schrödinger equations: Resonance-dominated and dispersion-dominated solutions
- STABLE DIRECTIONS FOR EXCITED STATES OF NONLINEAR SCHRÖDINGER EQUATIONS
- Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions
- Why are solitons stable?
- SELECTION OF THE GROUND STATE FOR NONLINEAR SCHRÖDINGER EQUATIONS
