  We study monopole solutions of the quantum exact low-energy effective N=2
super Yang-Mills theories of Seiberg and Witten. We find a first order
differential equation for the spatial dependence of the moduli and show that it
can be interpreted as an attractor equation. Numerically integrating this
equation, we try to address the question of what happens when one approaches
the quantum core of the monopole where the low energy effective theory breaks
down or, alternatively, if there are modified monopole solutions that do not
have a strongly coupled quantum core so that one may trust the solution not
only asymptotically.
