Vortex rings for the Gross-Pitaevskii equation

DOI10.4171/JEMS/2zbMath1091.35085OpenAlexW2075673239MaRDI QIDQ1432718

Fabrice Bethuel, Didier Smets, Giandomenico Orlandi

Publication date: 15 June 2004

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=6&iss=1&rank=2

zbMATH Keywords

finite energy solutions

Mathematics Subject Classification ID

Statistical mechanics of superconductors (82D55) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50) Traveling wave solutions (35C07) Ginzburg-Landau equations (35Q56)

Related Items

Travelling waves for the Gross-Pitaevskii equation in dimension larger than two, Invariant manifolds of traveling waves of the 3D Gross-Pitaevskii equation in the energy space, Decay for travelling waves in the Gross-Pitaevskii equation, Existence of vortex-free solutions in the Painlevé boundary layer of a Bose-Einstein condensate, Motion of concentration sets in Ginzburg-Landau equations., The Cauchy problem for the Gross--Pitaevskii equation, A uniqueness result for travelling waves in the Gross-Pitaevskii equation, Leapfrogging vortex rings for the three dimensional Gross-Pitaevskii equation, Vortex-filaments for inhomogeneous superconductors in three dimensions, Multiple branches of travelling waves for the Gross–Pitaevskii equation, Unnamed Item, Vortex structures for Klein-Gordon equation with Ginzburg-Landau nonlinearity, Asymptotic stability of the black soliton for the Gross–Pitaevskii equation, Vortex rings for the Gross-Pitaevskii equation in \(\mathbb R^3\), Smooth branch of rarefaction pulses for the nonlinear Schrödinger equation and the Euler-Korteweg system in 2d, Global existence for defocusing cubic NLS and Gross-Pitaevskii equations in three dimensional exterior domains, A uniqueness result for the two-vortex traveling wave in the nonlinear Schrödinger equation, Rotating multicomponent Bose-Einstein condensates, Existence and nonexistence of traveling waves for the Gross-Pitaevskii equation in tori, Convergence of the parabolic Ginzburg--Landau equation to motion by mean curvature, Multivortex Traveling Waves for the Gross--Pitaevskii Equation and the Adler--Moser Polynomials, Interacting helical traveling waves for the Gross-Pitaevskii equation, The spatial behavior of rotating two-component Bose-Einstein condensates, Rarefaction pulses for the nonlinear Schrödinger equation in the transonic limit, Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity, On the first critical field in the three dimensional Ginzburg-Landau model of superconductivity, Two-component Bose-Einstein condensates, Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity, Asymptotic behavior of critical points for a Gross-Pitaevskii energy, Phase separation of two-component Bose–Einstein condensates, Bose-Einstein condensates with non-classical vortex, Rotating two-component Bose-Einstein condensates, Convergence of Ginzburg-Landau functionals in three-dimensional superconductivity, Traveling vortex helices for Schrödinger map equations, Traveling wave solutions of the Schrödinger map equation, Asymptotics for the Ginzburg-Landau equation on manifolds with boundary under homogeneous Neumann condition, Traveling waves for some nonlocal 1D Gross-Pitaevskii equations with nonzero conditions at infinity, Compactons, A lower bound on the energy of travelling waves of fixed speed for the Gross-Pitaevskii equation, Travelling waves for the nonlinear Schrödinger equation with general nonlinearity in dimension two, The spinor Ginzburg-Landau model in dimension three, Travelling waves for the Gross-Pitaevskii equation. II, Orbital stability of traveling waves for the one-dimensional Gross-Pitaevskii equation, Multi-dimensional compactons and compact vortices, Vortex helices for the Gross-Pitaevskii equation, Generalized Adler--Moser Polynomials and Multiple Vortex Rings for the Gross--Pitaevskii Equation, Rotating 2N-vortex solutions to the Gross-Pitaevskii equation on S2, Collisions and phase-vortex interactions in dissipative Ginzburg-Landau dynamics, Finite energy traveling waves for the Gross-Pitaevskii equation in the subsonic regime, \(p\)-adic \(L\)-functions and unitary completions of representations of \(p\)-adic reductive groups, Limit at infinity for travelling waves in the Gross-Pitaevskii equation.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Orbital stability of standing waves for some nonlinear Schrödinger equations
• Stability theory of solitary waves in the presence of symmetry. I
• Asymptotics for the minimization of a Ginzburg-Landau functional
• The Cauchy problem in local spaces for the complex Ginzburg-Landau equation. II: Contraction methods
• Convergence of the parabolic Ginzburg--Landau equation to motion by mean curvature
• From Ginzburg-Landau to Gross-Pitaevskii
• The Jacobian and the Ginzburg-Landau energy
• A global theory of steady vortex rings in an ideal fluid
• Decay for travelling waves in the Gross-Pitaevskii equation
• Vortices for a variational problem related to superconductivity
• Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents
• On the first variation of a varifold
• A quantization property for static Ginzburg-Landau vortices
• estimates for solutions to the Ginzburg–Landau equation with boundary data in
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• On the stability theory of solitary waves
• Uniform estimates for the parabolic Ginzburg–Landau equation
• On the structure of the Sobolev space H1/2 with values into the circle
• Variational convergence for functionals of Ginzburg-Landau type
• Existence of steady vortex rings in an ideal fluid
• Ginzburg-Landau vortices
• Asymptotics for the Ginzburg-Landau equation in arbitrary dimensions