Adiabatic approximation for the motion of Ginzburg-Landau vortex filaments

DOI10.1007/s00220-021-04258-wOpenAlexW3213456021MaRDI QIDQ2071794

Jingxuan Zhang

Publication date: 31 January 2022

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.04984

zbMATH Keywords

adiabatic approximationvortex filamentsdispersive Ginzburg-Landau equation

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Statistical mechanics of superfluids (82D50) Ginzburg-Landau equations (35Q56)

Related Items

A generic framework of adiabatic approximation for nonlinear evolutions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stability of traveling waves of nonlinear Schrödinger equation with nonzero condition at infinity
• Derivation of an effective evolution equation for a strongly coupled polaron
• Effective dynamics of double solitons for perturbed mKdV
• A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations
• The Cauchy problem for the Gross--Pitaevskii equation
• Universality in mean curvature flow neckpinches
• Neck pinching dynamics under mean curvature flow
• Adiabatic limit and the slow motion of vortices in a Chern-Simons-Schrödinger system
• Geometric methods in the quantum many-body problem. Nonexistence of very negative ions
• On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
• Dynamics of Abelian Higgs vortices in the near Bogomolny regime
• The geodesic approximation for the Yang-Mills-Higgs equations
• Linear and nonlinear aspects of vortices. The Ginzburg-Landau model
• Invariant manifolds of traveling waves of the 3D Gross-Pitaevskii equation in the energy space
• The effective dynamics of the volume preserving mean curvature flow
• Convergence of the parabolic Ginzburg-Landau equation to motion by mean curvature
• Solitary wave dynamics in an external potential
• Effective dynamics of magnetic vortices
• Asymptotic Stability of Multi-soliton Solutions for Nonlinear Schrödinger Equations
• The Ginzburg-Landau equation III. Vortex dynamics
• Long-time behaviour of Ginzburg-Landau vortices
• Complex Ginzburg-Landau equations and dynamics of vortices, filaments, and codimension-2 submanifolds
• Adiabatic theorem for the Gross–Pitaevskii equation
• Neckpinch Dynamics for Asymmetric Surfaces Evolving by Mean Curvature Flow
• Variational Methods
• Effective dynamics of multi-vortices in an external potential for the Ginzburg–Landau gradient flow
• Ginzburg-Landau vortices
• Asymptotics for the Ginzburg-Landau equation in arbitrary dimensions