  We employ the non-linear realization techniques to relate the N=1 chiral, and
the N=2 vector multiplets to the Goldstone spin 1/2 superfield arising from
partial supersymmetry breaking of N=2 and N=3 respectively. In both cases, we
obtain a family of non-linear transformation laws realizing an extra
supersymmetry. In the N=2 case, we find an invariant action which is the low
energy limit of the supersymmetric Born-Infeld theory expected to describe a
D3-brane in six dimensions.
