  We investigate the localization problem of matter fields within the 5D
standing wave braneworld. In this model the brane emits anisotropic waves into
the bulk with different amplitudes along different spatial dimensions. We show
that in the case of increasing warp factor there exist the pure gravitational
localization of all kinds of quantum and classical particles on the brane. For
classical particles the anisotropy of the background metric is hidden, brane
fields exhibit standard Lorentz symmetry in spite of anisotropic nature of the
primordial 5D metric.
