Abstract
We show that the solutions of the Bogomolny equations for
the abelian Higgs model on a two-dimensional torus, can be expanded
in powers of a quantity 
measuring the departure of the
area from the critical area. This allows a precise determination of
the shape of the solutions for all magnetic fluxes and arbitrary
position of the Higgs field zeroes. The expansion is carried out to
51 orders for a couple of representative cases, including the unit
flux case. We analyse the behaviour of the expansion in the limit of
large areas, in which case the solutions approach those on the
plane. Our results suggest convergence all the way up to infinite
area.
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