  We derive a closed equation for the shape of the free surface of a magnetic
fluid subject to an external magnetic field. The equation is strongly non-local
due to the long range character of the magnetic interaction. We develop a
systematic multiple scale perturbation expansion in which the non-locality is
reduced to the occurrence of the Hilbert transform of the surface profile. The
resulting third order amplitude equation describing the slow modulation of the
basic pattern is shown to be purely local.
