The dynamics of a Hall plasma is considered under the conditions when
the equalization of the Lagrange invariant I = Omega/n (where Omega is
the vorticity due to the magnetic field B, which is transverse to the
direction of the plasma motion; and n is the plasma density) over the
plasma is caused by rapid oscillations. An equation for the ion motio
n with allowance for the electron rotational motion is obtained. The d
iscontinuous solutions are studied for the scales equal to the collisi
onless skin depth c/omega(pc).