Multiple Time Scale Dynamics in Coupled Ginzburg-Landau Equations

Localized structures in coupled Ginzburg–Landau equations

Coupled Complex Ginzburg-Landau equations describe generic features of the dynamics of coupled fields when they are close to a Hopf bifurcation leading to nonlinear oscillations. We study numerically this set of equations and find, within a particular range of parameters, the presence of uniformly propagating localized objects behaving as coherent structures. Some of these localized objects are...

Wave-unlocking transition in resonantly coupled complex Ginzburg-Landau equations.

We study the effect of spatial frequency forcing on standing-wave solutions of coupled complex Ginzburg-Landau equations. The model considered describes several situations of nonlinear counterpropagating waves and also of the dynamics of polarized light waves. We show that forcing introduces spatial modulations on standing waves which remain frequency locked with a forcing-independent frequency...

Asymptotic Behaviour of Time-dependent Ginzburg+Landau Equations of Superconductivity

In this paper, we establish the global fast dynamics for the time-dependent Ginzburg}Landau equations of superconductivity. We show the squeezing property and the existence of "nite-dimensional exponential attractors for the system. In addition we prove the existence of the global attractor in ̧2] ̧2 for the Ginzburg}Landau equations in two spatial dimensions. Copyright ( 1999 John Wiley & Sons, ...

Dynamics of Ginzburg-Landau vortices

Coarsening by Ginzburg-Landau Dynamics

We study slowly moving solutions of the real Ginzburg-Landau equation on the line, by a method due to J. Carr and R.L. Pego. These are functions taking alternately positive or negative values on large intervals. A consequence of our approach is that we can propose a rigorous derivation of a stochastic model of coarsening by successive elimination of the smallest interval, which was described in...