On the solutions of the one-dimensional Ginzburg-Landau equations for superconductivity

This paper gives a complete description of the solutions of the one-dimensi onal Ginzburg-Landau equations which model superconductivity phenomena in i nfinite slabs. We investigate this problem over the entire range of physica lly important parameters: a the size of the slab, kappa the Ginzburg-Landau parameter, and Ire, the exterior magnetic field. We do extensive numerical computations using the software AUTO, and determine the number, symmetry a nd stability of solutions for all values of the parameters. In particular, our experiments reveal the existence of two key-points in parameter space w hich play a central role in the formation of the complicated patterns by me ans of bifurcation phenomena. Our global description also allows us to sepa rate the various physically important regimes, to classify previous results in each regime according to the values of the parameters and to derive new open problems. In addition, our investigation provides new insight into th e problem of differentiating between the types of superconductors in terms of the parameters. (C) 1999 Published by Elsevier Science B.V. All rights r eserved.