  The propagation of classical wave in disordered media at the Anderson
localization transition is studied. Our results show that the classical waves
may follow a different scaling behavior from that for electrons. For electrons,
the effect of weak localization due to interference of recurrent scattering
paths is limited within a spherical volume because of electron-electron or
electron-phonon scattering, while for classical waves, it is the sample
geometry that determine the amount of recurrent scattering paths that
contribute. It is found that the weak localization effect is weaker in both
cubic and slab geometry than in spherical geometry. As a result, the averaged
static diffusion constant D(L) scales like ln(L)/L in cubic or slab geometry
and the corresponding transmission follows <T(L)>~ln L/L^2. This is in contrast
to the behavior of D(L)~1/L and <T(L)>~1/L^2 obtained previously for electrons
or spherical samples. For wave dynamics, we solve the Bethe-Salpeter equation
in a disordered slab with the recurrent scattering incorporated in a
self-consistent manner. All of the static and dynamic transport quantities
studied are found to follow the scaling behavior of D(L). We have also
considered position-dependent weak localization effects by using a plausible
form of position-dependent diffusion constant D(z). The same scaling behavior
is found, i.e., <T(L)>~ln L/L^2.
