Global structure of exact cosmological solutions in the brane world

We find the explicit coordinate transformation which links two exact cosmological solutions of the brane world which have been recently discovered. This means that both solutions are exactly the same as each other. One of the two solutions is described by the motion of a domain wall in the well-known five-dimensional Schwarzshild-AdS spacetime. Hence, we can easily understand the region covered by the coordinate used by another solution.