%0 Journal Article %T Unidimensional model of the ad-atom diffusion on a substrate submitted to a standing acoustic wave II. Solutions of the ad-atom motion equation %A Nicolas Combe %A C. Taillan %A J. Morillo %J Physics %D 2012 %I arXiv %X 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. %U http://arxiv.org/abs/1203.2812v1