• Corpus ID: 236924438

Entire solutions of the magnetic Ginzburg-Landau equation in $\mathbb{R}^4$

  title={Entire solutions of the magnetic Ginzburg-Landau equation in \$\mathbb\{R\}^4\$},
  author={Yong Liu and Xinan Ma and Juncheng Wei and Wangze Wu},
We construct entire solutions of the magnetic Ginzburg-Landau equations in dimension 4 using Lyapunov-Schmidt reduction. The zero set of these solutions are close to the minimal submanifolds studied by Arezzo-Pacard[1]. We also show the existence of a saddle type solution to the equations, whose zero set consists of two vertical planes in R. These two types of solutions are believed to be energy minimizers of the corresponding energy functional and lie in the same connect component of the… 



Multi-Vortex Non-radial Solutions to the Magnetic Ginzburg-Landau Equations

We show that there exists multi-vortex, non-radial, finite energy solutions to the magnetic Ginzburg-Landau equations on all of $${\mathbb{R}^2}$$ . We use Lyapunov-Schmidt reduction to construct

Multi-Vortex Solutions to Ginzburg–Landau Equations with External Potential

We consider the existence of multi-vortex solutions to the Ginzburg–Landau equations with external potential on $${\mathbb{R}^2}$$ . These equations model equilibrium states of superconductors and

Complex Ginzburg-Landau equations and dynamics of vortices, filaments, and codimension-2 submanifolds

Here we study the asymptotic behavior of solutions to the complex Ginzburg-Landau equations and their associated heat flows in arbitrary dimensions when the Ginzburg-Landau parameter tends to

Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents

Abstract.There is an obvious topological obstruction for a finite energy unimodular harmonic extension of a S1-valued function defined on the boundary of a bounded regular domain of Rn. When such

Multivortex Traveling Waves for the Gross-Pitaevskii Equation and the Adler-Moser Polynomials

It is expected that this assumption that the corresponding Adler-Moser polynomial has no repeated root holds for any $N\in\mathbb{N}$.

Asymptotics for the Ginzburg–Landau Equation in Arbitrary Dimensions

Let Ω be a bounded, simply connected, regular domain of RN, N⩾2. For 0<e<1, let ue: Ω→C be a smooth solution of the Ginzburg–Landau equation in Ω with Dirichlet boundary condition ge, i.e.,[formula]

Regularity of flat level sets in phase transitions

We consider local minimizers of the Ginzburg-Landau energy functional ∫1/2|∇u| 2 +1/4(1-u 2 ) 2 dx and prove that, if the 0 level set is included in a flat cylinder then, in the interior, it is

The Stability of Magnetic Vortices

We study the linearized stability of n-vortex solutions of the magnetic Ginzburg-Landau (or Abelian-Higgs) equations. We prove that the fundamental vortices (n=1,-1) are stable for all values of the

Ginzburg-Landau Vortices

The mathematics in this book apply directly to classical problems in superconductors, superfluids and liquid crystals. It should be of interest to mathematicians, physicists and engineers working on