  Stationary solutions of the Chern-Simons effective field theory for the
fractional quantum Hall systems with edges are presented for Hall bar, disk and
annulus. In the infinitely long Hall bar geometry (non compact case), the
charge density is shown to be monotonic inside the sample. In sharp contrast,
spatial oscillatory modes of charge density are found for the two circular
geometries, which indicate that in systems with compact geometry, charge and
current exist also far from the edges.
