TY - JOUR

T1 - MULTIPLE TIME SCALE DYNAMICS IN COUPLED GINZBURG-LANDAU EQUATIONS

AU - Lin, Fanghua

AU - Lin, Tai Chia

N1 - Funding Information:
Acknowledgement. The research of the first author is partially supported by the NSF grant DMS-0201443.The research of the second author is partially supported by a research Grant (NSC92-2115-M-194-014) from NSC of Taiwan.A big portion of the work was carried out while both authors were visiting the Center of the Mathematical Sciences at the Zhejiang University,Hangzhou,China.They wish to thank the center for the warm hospitality.
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 -