The plan of the paper is as follows. In section II we review the results for kink-like backgrounds in a flat extra dimension with no gravity. We then generalize these to include a warped gravitational background, but with no gravitational backreaction from the kink- scalar itself. In section IV we consider the coupled system of multiple scalar fields in the presence of gravity, and as a special case consider a kink field with Dirichlet boundary conditions and another scalar whose purpose is to stabilize the whole configuration. We write the background equations for such a system and show graphically how non-linearities allow a given action to have multiple static solutions. In the final section we take the first steps towards studying the question of the stability of these static configurations by deriving the complete set of equations for scalar and grav- itational perturbations around a given static background. The general procedure is quite complex and involves extended theorems of oscillation theory appropriate to the type of eigenvalue problem we are lead to, namely a matrix Sturm-Liouville problem. We therefore reserve a complete study of the stability of the general system for future work. In [40, 41] a 5D flat scenario including one real scalar field with an arbitrary scalar potential was studied and the general conditions for the existence and perturbative stability of static, nontrivial, background scalar field configurations were presented. In this section we briefly review the main results and slightly extend the discussion of the energy densities of different kink configurations. Consider a real scalar field in 5 dimensions (labeled by indices M, N, . . . = 0 , 1 , 2 , 3 , 5) with a flat background metric, and defined by the action The extra dimension is compactified on an S$_{1}$/Z$_{2}$ orbifold with the scalar field φ ( x, y ) being odd under Z$_{2}$ reflections along the extra coordinate x $^{5}$≡ y (i.e. φ ( x, y ) = − φ ( x, − y )). Here the orbifold interval is defined as [0 , πR ], with its size πR assumed to be fixed. The potential V ( φ ) must then be invariant under the discrete symmetry φ → − φ , and is chosen to have at least two degenerate global minima at φ = ± v , with v = 0. To simplify notation, we will also choose the potential to vanish at φ =0. S = ∫ d $^{5}$x [ 1 2 η $^{MN}$( ∂$_{M}$ φ ) ∂$_{N}$φ − V ( φ ) ] . (1) 3 II. KINKED SCALARS IN FLAT EXTRA DIMENSIONS