Hg. Kaper et P. Takac, AN EQUIVALENCE RELATION FOR THE GINZBURG-LANDAU EQUATIONS OF SUPERCONDUCTIVITY, Zeitschrift fur angewandte Mathematik und Physik, 48(4), 1997, pp. 665-675
Gauge invariance is used to establish an equivalence relation between
solutions of the time-independent and time-dependent Ginzburg-Landau e
quations that describe the same physical state of a superconductor. Th
e equivalence relation shows how equilibrium configurations are obtain
ed as large-time asymptotic limits of solutions of the time-dependent
Ginzburg-Landau equations.