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

Small amplitude, long waves traveling over the surface of a current-carryin g metal thin film are studied. The equation of motion for the metal surface is determined in the limit of high applied currents, when surface electrom igration is the predominant cause of adatom motion. If the surface height h is independent of the transverse coordinate y, the equation of motion redu ces to the Korteweg-de Vries equation. One-dimensional solitons (i.e., thos e with h independent of y) are shown to be unstable against perturbations t o their shape with small transverse wavevector. (C) 2001 Elsevier Science B .V. All rights reserved.