Transverse instability of solitons propagating on current-carrying metal thin films

Small amplitude, long waves traveling 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.