Vortex dynamics in d-wave superconductors

We study the dynamics of vortices in the time-dependent Ginzburg-Landau equation for d-wave superconductors. Under suitable assumptions on the coefficients of the time-dependent Ginzburg-Landau equation and some assumptions on the vortex structures, the asymptotic motion equations of vortices are derived as a system of ordinary differential equations. Furthermore, the asymptotic motion equations of vortices predict the attracting of two degree-one vortices in d-wave superconductors which is observed by Du [SIAM J. Appl. Math. 59 (1999) 1225] by numerical simulation. (C) 2001 Elsevier Science B.V. All rights reserved.