TY - JOUR
T1 - MULTIPLE TIME SCALE DYNAMICS IN COUPLED GINZBURG-LANDAU EQUATIONS
AU - Lin, Fanghua
AU - Lin, Tai Chia
N1 - Publisher Copyright:
© 2003 International Press
PY - 2003
Y1 - 2003
N2 - Using a rather simple model of coupled, time-dependent Ginzburg-Landau equations with two order parameters, we demonstrate that the total Hamiltonian 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 (fractional degree vortices) and paired vortices. In particular, we rigorously show, after an initial time period of adjusting, the domain walls start to move according the 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.
AB - Using a rather simple model of coupled, time-dependent Ginzburg-Landau equations with two order parameters, we demonstrate that the total Hamiltonian 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 (fractional degree vortices) and paired vortices. In particular, we rigorously show, after an initial time period of adjusting, the domain walls start to move according the 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.
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U2 - 10.4310/CMS.2003.v1.n4.a3
DO - 10.4310/CMS.2003.v1.n4.a3
M3 - Article
AN - SCOPUS:67349169367
SN - 1539-6746
VL - 1
SP - 671
EP - 695
JO - Communications in Mathematical Sciences
JF - Communications in Mathematical Sciences
IS - 4
ER -