  In this paper we use the anholonomic frames method to construct exact
solutions for vacuum 5D gravity with metrics having off-diagonal components.
The solutions are in general anisotropic and possess interesting features such
as an anisotropic warp factor with respect to the extra dimension, or a
gravitational scaling/running of some of the physical parameters associated
with the solutions. A certain class of solutions are found to describe
Schwarzschild black holes which ``solitonically'' propagate in spacetime. The
solitonic character of these black hole solutions arises from the embedding of
a 3D soliton configuration (e.g. the soliton solutions to the
Kadomtsev-Petviashvily or sine-Gordon equations) into certain ansatz functions
of the 5D metric. These solitonic solutions may either violate or preserve
local Lorentz invariance. In addition there is a connection between these
solutions and noncommutative field theory.
