Galilean exotic planar supersymmetries and nonrelativistic supersymmetric wave equations

We describe the general class of N-extended D=(2+1) Galilean supersymmetries obtained, respectively, from the N-extended D=3 Poincaré superalgebras with maximal sets of central charges. We confirm the consistency of supersymmetry with the presence of the 'exotic' second central charge θ. We show further how to introduce a N=2 Galilean superfield equation describing nonrelativistic spin 0 and spin 12 free particles.