  The gravity coupling of the symmetric space sigma model is studied in the
solvable Lie algebra parametrization. The corresponding Einstein's equations
are derived and the energy-momentum tensor is calculated. The results are used
to derive the dynamical equations of the warped 5D geometry for localized bulk
scalar interactions in the framework of thick brane world models. The Einstein
and scalar field equations are derived for flat brane geometry in the context
of minimal and non-minimal gravity-bulk scalar couplings.
