Abstract 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, we find the dilaton field to be a kink in the fifth dimension.