GLYPH<B9>GLYPH<BF> GLYPH<B9>GLYPH<BE>GLYPH<BA>GLYPH<BH> GLYPH<B9>GLYPH<BE> GLYPH<B9>GLYPH<BD>GLYPH<BA>GLYPH<BH> GLYPH<B9>GLYPH<BD> GLYPH<B9>GLYPH<BC>GLYPH<BA>GLYPH<BH> GLYPH<BC> GLYPH<BC>GLYPH<BA>GLYPH<BH> GLYPH<BC> GLYPH<BD> GLYPH<BE> GLYPH<BF> GLYPH<BG> GLYPH<BH> GLYPH<BI> [ M 3 / 2 ∗ ] GLYPH<B4>GLYPH<BT>GLYPH<B5> y [ M − 1 ∗ ] φ ( y ) χ ( y ) σ ( y ) GLYPH<BD> GLYPH<BE> GLYPH<BF> GLYPH<BG> GLYPH<BH> GLYPH<BI> GLYPH<B4>GLYPH<BU>GLYPH<B5> φ ( y ) χ ( y ) σ ( y ) FIG. 4: Profiles of the scalar backgrounds φ ( y ) and χ ( y ) as well as the warp factor σ ( y ), showing the two possible solutions (panels A and B) to the same boundary value problem defined by the physical parameters m 2 χ = − 0 . 5 M 2 $_{∗}$, µ 2 1 = − 0 . 25 M 2 $_{∗}$, µ 2 = − 8 M 2 $_{∗}$, Σ$_{1}$ = − 2 M 4 $_{∗}$, Σ$_{2}$ = 0 . 52 M 4 $_{∗}$, m 2 φ = 0 . 5 M 2 $_{∗}$, λ = 2 M − 1 ∗ , and Λ = 0. In our more general setting, including gravity and a stabilization field, we find numerically that there exists more than one solution for the same Lagrangian in a large portion of the parameters space. In Fig. 6 we show two such solutions. Note that these solutions would be extremely difficult to discover by randomly guessing initial-boundary conditions. To be more methodical we follow the same procedure as before to find level-curves of the final- boundary conditions, shown in Fig. 7. Again, solutions to a particular action will be given by the intersection of the appropriate contours for the brane mass squared µ 2 and brane tension Σ$_{2}$. As can be seen, there are regions in which some contours intersect at more than one point, showing that multiple solutions for the same action are possible as expected. In 18