  The motion of a thin layer of granular material on a plate undergoing
sinusoidal vibrations is considered. We develop equations of motion for the
local thickness and the horizontal velocity of the layer. The driving comes
from the violent impact of the grains on the plate. A linear stability theory
reveals that the waves are excited non-resonantly, in contrast to the usual
Faraday waves in liquids. Together with the experimentally observed continuum
scaling, the model suggests a close connection between the neutral curve and
the dispersion relation of the waves, which agrees quite well with experiments.
For strong hysteresis we find localized oscillon solutions.
