Recent results for the Landau-Lifshitz equation

DOI10.1007/s40324-021-00254-1zbMath1490.35407arXiv2011.01692OpenAlexW3166541937MaRDI QIDQ2150692

Publication date: 30 June 2022

Published in: S\(\vec{\text{e}}\)MA Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.01692

zbMATH Keywords

self-similar solutions nonlinear Schrödinger equation solitons Landau-Lifshitz-Gilbert equation ferromagnetic spin chain asymptotic regimes

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Statistical mechanics of magnetic materials (82D40)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Asymptotic stability in energy space for dark solitons of the Landau-Lifshitz equation
Geometric flows with rough initial data
Landau-Lifshitz equation, uniaxial anisotropy case: theory of exact solutions
Stability in the energy space for chains of solitons of the Landau-Lifshitz equation
Error bounds for the (KdV)/(KP-I) and (gKdV)/(gKP-I) asymptotic regime for nonlinear Schrödinger type equations
Stability in the energy space for chains of solitons of the one-dimensional Gross-Pitaevskii equation
Global well-posedness of the Landau-Lifshitz-Gilbert equation for initial data in Morrey spaces
Global Schrödinger maps in dimensions \(d\geq 2\): small data in the critical Sobolev spaces
Selfsimilar expanders of the harmonic map flow
Scattering for 1D cubic NLS and singular vortex dynamics
Well-posedness for the heat flow of harmonic maps and the liquid crystal flow with rough initial data
Stability of two soliton collision for nonintegrable gKdV equations
On the stability of a singular vortex dynamics
On the global well-posedness of the one-dimensional Schrödinger map flow
Self-similar solutions for the Schrödinger map equation
Schrödinger maps and anti-ferromagnetic chains
Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
Nonuniqueness for the heat flow of harmonic maps
On the Dirac delta as initial condition for nonlinear Schrödinger equations
Exact solutions of semiclassical non-characteristic Cauchy problems for the sine-Gordon equation
A survey on the numerics and computations for the Landau-Lifshitz equation of micromagnetism
On the linear wave regime of the Gross-Pitaevskii equation
Partial differential equations. III: Nonlinear equations.
Orbital stability of traveling waves for the one-dimensional Gross-Pitaevskii equation
Nonlinear partial differential equations. Asymptotic behavior of solutions and self-similar solutions
Stability theory of solitary waves in the presence of symmetry. I
Schrödinger flow of maps into symplectic manifolds
Existence of the self-similar solutions in the heat flow of harmonic maps
Singularities of first kind in the harmonic map and Yang-Mills heat flows
Global wellposedness for 1D nonlinear Schrödinger equation for data with an infinite \(L^2\) norm
The sine-Gordon regime of the Landau-Lifshitz equation with a strong easy-plane anisotropy
Singularity formation for the 1-D cubic NLS and the Schrödinger map on \(\mathbb{S}^2\)
Uniqueness of Schrödinger flow on manifolds
On the continuous limit for a system of classical spins
On the ill-posedness of some canonical dispersive equations.
Stability and asymptotic stability for subcritical gKdV equations
The cubic Schrödinger regime of the Landau-Lifshitz equation with a strong easy-axis anisotropy
Self-similar shrinkers of the one-dimensional Landau-Lifshitz-Gilbert equation
Traveling waves for some nonlocal 1D Gross-Pitaevskii equations with nonzero conditions at infinity
Long wave limit for Schrödinger maps
On Navier-Stokes-Korteweg and Euler-Korteweg systems: application to quantum fluids models
Inelastic interaction of nearly equal solitons for the quartic gKdV equation
Stability of the self-similar dynamics of a vortex filament
Asymptotic stability of solitons of the gKdV equations with general nonlinearity
Stability in \(H^1\) of the sum of \(K\) solitary waves for some nonlinear Schrödinger equations
Global solvability of the Cauchy problem for the Landau-Lifshitz-Gilbert equation in higher dimensions
Nonexistence of Shrinkers for the Harmonic Map Flow in Higher Dimensions
Global Well-Posedness for a Nonlocal Gross–Pitaevskii Equation with Non-Zero Condition at Infinity
The KdV/KP-I Limit of the Nonlinear Schrödinger Equation
The fascinating world of the Landau–Lifshitz–Gilbert equation: an overview
Madelung, Gross–Pitaevskii and Korteweg
Shrinkers, expanders, and the unique continuation beyond generic blowup in the heat flow for harmonic maps between spheres
Construction of a spectrally stable self-similar blowup solution to the supercritical corotational harmonic map heat flow
An Approximation Scheme for Schrödinger Maps
On the Korteweg–de Vries Long-Wave Approximation of the Gross–Pitaevskii Equation II
Orbital stability of the black soliton for the Gross-Pitaevskii equation
Another Report on Harmonic Maps
On global weak solutions for Landau-Lifshitz equations: Existence and nonuniqueness
Schrödinger maps
On Uniqueness for the Harmonic Map Heat Flow in Supercritical Dimensions
On the asymptotic stability in the energy space for multi-solitons of the Landau-Lifshitz equation
Self-similar solutions of the localized induction approximation: singularity formation
Asymptotic stability of solitons of the subcritical gKdV equations revisited
Formation of Singularities and Self-Similar Vortex Motion Under the Localized Induction Approximation†
The stability of localized solutions of Landau‐Lifshitz equations
Existence of expanders of the harmonic map flow
On self-similar solutions of the vortex filament equation
Fractal solutions of linear and nonlinear dispersive partial differential equations
Self-similar solutions of the one-dimensional Landau–Lifshitz–Gilbert equation
The Cauchy problem for the Landau–Lifshitz–Gilbert equation in BMO and self-similar solutions
Minimal Energy for the Traveling Waves of the Landau--Lifshitz Equation
Finite Time singularity of the Landau-Lifshitz-Gillbert Equation
Schrodinger Maps and their Associated Frame Systems
The role of self-similarity in singularities of partial differential equations
Existence and properties of travelling waves for the Gross-Pitaevskii equation
A soliton on a vortex filament
Well-posedness for the Navier-Stokes equations

This page was built for publication: Recent results for the Landau-Lifshitz equation