The ad-atom dynamic equation, a Langevin type equation is analyzed and solved
using some non-linear analytical and numerical tools. We noticeably show that
the effect of the surface acoustic wave is to induce an effective potential
that governs the diffusion of the ad-atom: the minima of this effective
potential correspond to the preferential sites in which the ad-atom spends more
time. The strength of this effective potential is compared to the destructuring
role of the thermal diffusion and to the crystalline potential induced by the
substrate