  Small amplitude, long waves travelling over the surface of a current-carrying
metal thin film are studied. The equation of motion for the metal surface is
determined in the limit of high applied currents, when surface electromigration
is the predominant cause of adatom motion. If the surface height h is
independent of the transverse coordinate y, the equation of motion reduces to
the Korteweg-de Vries equation. One-dimensional solitons (i.e., those with h
independent of y) are shown to be unstable against perturbations to their shape
with small transverse wavevector.
