Continuum description of vibrated sand

The motion of a thin layer of granular material on a plate undergoing sinus oidal vibrations is considered. We develop equations of motion for the loca l thickness and the horizontal velocity of the layer. The driving comes fro m the violent impact of the grains on the plate. A Linear stability theory reveals that the waves are excited nonresonantly, in contrast to the usual Faraday waves in liquids. Together with the experimentally observed continu um scaling, the model suggests a close connection between the neutral curve and the dispersion relation of the waves, which agrees quite well with exp eriments. For strong hysteresis we find localized oscillon solutions.