  We add a Gauss-Bonnet term to the Einstein-Hilbert action and study the
recent proposal to solve the cosmological constant problem. We also consider
the possibility of adding a dilaton potential to the action. In the absence of
supersymmetry, we obtain first order Bogomol'nyi equation as a
solution-generating method in our scenario. When the coefficient of the
Gauss-Bonnet term is positive, the dilaton potential is bounded below. Assuming
a simple double-well potential, the dilaton field is found to be a kink in the
fifth dimension.
