  We show that the thin wall limit of the thick domain wall associated with a
sine-Gordon soliton in a single non-compactified patch of 5-dimensional
spacetime explicitly yields the Randall-Sundrum localized gravity two patch
brane, with its discrete $Z_2$ symmetry arising from the discrete symmetry of
the potential, and with the thin Minkowski brane
$\Lambda_5+\kappa^2_5\Lambda^2_b/6=0$ relation between bulk and brane
cosmological constants arising naturally without any need for fine tuning.
Additionally we show that for an embedded thin de Sitter brane, localization of
gravity is again possible provided the 5-space is compactified, with the now
non-zero net cosmological constant $\Lambda_5+\kappa^2_5\Lambda^2_b/6$ on the
brane being found to vary inversely with the compactification radius.
