GLYPH<BC>GLYPH<BA>GLYPH<BD> GLYPH<BC>GLYPH<BA>GLYPH<BD>GLYPH<BH> GLYPH<BC>GLYPH<BA>GLYPH<BE> GLYPH<BC>GLYPH<BA>GLYPH<BE>GLYPH<BH> GLYPH<BC>GLYPH<BA>GLYPH<BF> GLYPH<BC>GLYPH<BA>GLYPH<BF>GLYPH<BH> GLYPH<BC>GLYPH<BA>GLYPH<BG> GLYPH<BC>GLYPH<BA>GLYPH<BG>GLYPH<BH> GLYPH<BC>GLYPH<BA>GLYPH<BD> GLYPH<BC>GLYPH<BA>GLYPH<BE> GLYPH<BC>GLYPH<BA>GLYPH<BF> GLYPH<BC>GLYPH<BA>GLYPH<BG> GLYPH<BC>GLYPH<BA>GLYPH<BH> GLYPH<BC>GLYPH<BA>GLYPH<BI> χ ′ 1 [ M 5 / 2 ∗ ] φ ′ 1 [ M 5 / 2 ∗ ] µ 2 Σ$_{2}$ (4) R GLYPH<B9>GLYPH<BD>GLYPH<BC> GLYPH<B9>GLYPH<BK> GLYPH<B9>GLYPH<BI> GLYPH<B9>GLYPH<BG> GLYPH<B9>GLYPH<BE> GLYPH<BC> GLYPH<BC>GLYPH<BA>GLYPH<BH>GLYPH<BI> GLYPH<BC>GLYPH<BA>GLYPH<BH>GLYPH<BI> GLYPH<BC>GLYPH<BA>GLYPH<BH>GLYPH<BG> GLYPH<BC>GLYPH<BA>GLYPH<BH>GLYPH<BE> GLYPH<BC>GLYPH<BA>GLYPH<BH> GLYPH<BC>GLYPH<BA>GLYPH<BG>GLYPH<BK> GLYPH<BC>GLYPH<BA>GLYPH<BH> GLYPH<BC> GLYPH<B9>GLYPH<BC>GLYPH<BA>GLYPH<BH> FIG. 5: Level-curves of µ 2 and Σ$_{2}$ in the φ ′ $_{1}$- χ ′ 1 parameter space for example 1 with m 2 χ = − 0 . 5 M 2 $_{∗}$, µ 2 1 = − 0 . 25 M 2 $_{∗}$, Σ$_{1}$ = − 2 M 4 $_{∗}$, m 2 φ = 0 . 5 M 2 $_{∗}$, λ = 2 M − 1 ∗ , and Λ = 0. Circled are two points in the φ ′ $_{1}$- χ ′ 1 parameter space with the same values of µ 2 and Σ$_{2}$, corresponding to two solutions with the same Lagrangian (plotted in Fig. 4). particular, we again circle two such points, corresponding to the solutions plotted in Figs. 6. As an interesting remark, note that both of these particular solutions happen to lie near the region of parameter space where the 4D cosmological constant vanishes. Having shown how different nontrivial static field configurations exist in warped extra dimensions, the next question to ask is whether these solutions are stable. As we reviewed in section II, in the case of flat extra dimensions there exist [41] techniques for determining the stability of such solutions. Indeed, for certain potentials, in that case perturbative stability V. STABILITY OF SOLUTIONS 19