When an electrical current passes through a piece of solid metal, collisions between the conduction electrons and the metal atoms at the surface lead to drift of these atoms. The free surface of a metal therefore moves and deforms in response to the electrical current flowing through it (albeit very slowly!)
If the anisotropy of the metal is negligible, solitons can propagate over the free surface of a current-carrying metal thin film. The equation of motion for one-dimensional small-amplitude long waves is the KdV equation. If the anisotropy is strong, on the other hand, shocks can form and the equation of motion is the Burgers equation. The generalization of these results to two-dimensional disturbances will also be discussed.