  Due to the effects of surface electromigration, waves can propagate over the
free surface of a current-carrying metallic or semiconducting film of thickness
h_0. In this paper, waves of finite amplitude, and slow modulations of these
waves, are studied. Periodic wave trains of finite amplitude are found, as well
as their dispersion relation. If the film material is isotropic, a wave train
with wavelength lambda is unstable if lambda/h_0 < 3.9027..., and is otherwise
marginally stable. The equation of motion for slow modulations of a finite
amplitude, periodic wave train is shown to be the nonlinear Schrodinger
equation. As a result, envelope solitons can travel over the film's surface.
