Self-dual Ginzburg-Landau vortices in a disc

We study the properties of the Ginzburg-Landau model in the self-dual point for a two-dimensional finite system. By a numerical calculation we analyse the solutions of the Euler-Lagrange equations for a cylindrically symmetri c ansatz, We also study the self-dual equations for this case. We find that the minimal energy configurations are not given by the Bogomol'nyi equatio ns but by solutions to the Euler-Lagrange ones. With a simple approximation scheme we reproduce the result of the numerical calculation.