  This paper gives a complete description of the solutions of the one
dimensional Ginzburg-Landau equations which model superconductivity phenomena
in infinite slabs. We investigate this problem over the entire range of
physically important parameters: $a$ the size of the slab, $\kappa$ the
Ginzburg-Landau parameter, and $h_0$, the exterior magnetic field. We do
extensive numerical computations using the software AUTO, and determine the
number, symmetry and stability of solutions for all values of the parameters.
In particular, our experiments reveal the existence of two key-points in
parameter space which play a central role in the formation of the complicated
patterns by means of bifurcation phenomena. Our global description also allows
us to separate 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 the
problem of differentiating between the types of superconductors in terms of the
parameters.
