  The class of non-stationary braneworld models generated by the coupled
gravitational and scalar fields is reviewed. The model represents a brane in a
space-time with single time and one large (infinite) and several small
(compact) space-like extra dimensions. In some particular cases the model has
the solutions corresponding to the bulk gravi-scalar standing waves bounded by
the brane. Pure gravitational localization mechanism of matter particles on the
node of standing waves, where the brane is placed, is discussed. Cosmological
applications of the model also considered.
