Bifurcating Vortex Solutions of the Complex Ginzburg-landau Equation
نویسنده
چکیده
It is shown that the complex Ginzburg-Landau (CGL) equation on the real line admits nontrivial 2-periodic vortex solutions that have 2n simple zeros (\vortices") per period. The vortex solutions bifurcate from the trivial solution and inherit their zeros from the solution of the linearized equation. This result rules out the possibility that the vortices are determining nodes for vortex solutions of the CGL equation.
منابع مشابه
Some new exact traveling wave solutions one dimensional modified complex Ginzburg- Landau equation
In this paper, we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the one-dimensional modified complex Ginzburg-Landau equation by using the $ (G'/G) $ expansion method, homogeneous balance method, extended F-expansion method. By using homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by j...
متن کاملExact solutions of the 2D Ginzburg-Landau equation by the first integral method
The first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to non integrable equations as well as to integrable ones. In this paper, the first integral method is used to construct exact solutions of the 2D Ginzburg-Landau equation.
متن کاملVortex Pinning with Bounded Fields for the Ginzburg–landau Equation
– We investigate vortex pinning in solutions to the Ginzburg–Landau equation. The coefficient, a(x), in the Ginzburg–Landau free energy modeling non-uniform superconductivity is nonnegative and is allowed to vanish at a finite number of points. For a sufficiently large applied magnetic field and for all sufficiently large values of the Ginzburg–Landau parameter κ = 1/ε, we show that minimizers ...
متن کاملOn compound vortices in a two-component Ginzburg-Landau functional
We study the structure of vortex solutions in a Ginzburg–Landau system for two complex valued order parameters. We consider the Dirichlet problem in the disk in R2 with symmetric, degree-one boundary condition, as well as the associated degree-one entire solutions in all of R2. Each problem has degree-one equivariant solutions with radially symmetric profile vanishing at the origin, of the same...
متن کاملLimiting Vorticities for the Ginzburg-landau Equations
We study the asymptotic limit of solutions of the Ginzburg-Landau equations in two dimensions with or without magnetic field. We first study the Ginzburg-Landau system with magnetic field describing a superconductor in an applied magnetic field, in the “London limit” of a Ginzburg-Landau parameter κ tending to ∞. We examine the asymptotic behavior of the “vorticity measures” associated to the v...
متن کامل