Communications in Mathematical Sciences

Multiple Time Scale Dynamics in Coupled Ginzburg-Landau Equations

Fangua Lin and Tai-Chia Lin

Abstract

Using a rather simple model of coupled, time-dependent Ginzburg-Landau equations with two order parameters, we demonstrate that the total Hamilitonian energy of the system contains at least three levels describing point vortices, domain walls and configurations. The global in time dynamics contain then also at least three different time scales for nontrivial motions of domain walls, boundaries of domain walls (frational degree vortices) and paired vortices. In particular, we rigorously show, after an intial time period of adjusting, the domain walls start to move according to motion by the mean-curvature that straighten out the domain walls while the boundaries of such domain walls are essentially fixed. After this motion is completed, the fractional degree vortices begin to move at the next time scale. The motion is relatively simple as it is of constant speed and toward each other to form vortex pairs. Finally, these vortex pairs may move in the final time scale very much like the ordinary vortices in a single time-dependent Ginzburg-Laudau equation.

Article information

Source
Commun. Math. Sci., Volume 1, Number 4 (2003), 671-695.

Dates
First available in Project Euclid: 24 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.cms/1119655351

Mathematical Reviews number (MathSciNet)
MR2041453

Zentralblatt MATH identifier
1160.82368

Citation

Lin, Fangua; Lin, Tai-Chia. Multiple Time Scale Dynamics in Coupled Ginzburg-Landau Equations. Commun. Math. Sci. 1 (2003), no. 4, 671--695. https://projecteuclid.org/euclid.cms/1119655351


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