  We consider a 5D BPS dilatonic two brane model which reduces to the
Randall-Sundrum model or the Horava-Witten theory for a particular choice of
parameters. Recently new dynamical solutions were found by Chen et al., which
describe a moduli instability of the warped geometry. Using a 4D effective
theory derived by solving the 5D equations of motion, based on the gradient
expansion method, we show that the exact solution of Chen et. al. can be
reproduced within the 4D effective theory and we identify the origin of the
moduli instability. We revisit the gradient expansion method with a new metric
ansatz to clarify why the 4D effective theory solution can be lifted back to an
exact 5D solution. Finally we argue against a recent claim that the 4D
effective theory allows a much wider class of solutions than the 5D theory and
provide a way to lift solutions in the 4D effective theory to 5D solutions
perturbatively in terms of small velocities of the branes.
