  A series of exact BPS solutions are found for single and double domain walls
in N=2 supersymmetric (SUSY) QED for finite gauge coupling constants. Vector
fields are found to be massive, although it is localized on the wall. Massless
modes can be assembled into a chiral scalar multiplet of the preserved N=1
SUSY, after an appropriate gauge choice. The low-energy effective Lagrangian
for the massless fields is obtained for the finite gauge coupling. The
inter-wall force is found to be much stronger than the known infinite coupling
case. The previously proposed expansion in inverse powers of the gauge coupling
has pathological oscillations, and does not converge to the correct finite
coupling result.
