  Domain wall solutions of $d$-dimensional gravity coupled to a dilaton field
$\sigma$ with an exponential potential $\Lambda e^{-\lambda\sigma}$ are shown
to be governed by an autonomous dynamical system, with a transcritical
bifurcation as a function of the parameter $\lambda$ when $\Lambda<0$. All
phase-plane trajectories are found exactly for $\lambda=0$, including
separatrices corresponding to walls that interpolate between $adS_d$ and
$adS_{d-1} \times\bR$, and the exact solution is found for $d=3$. Janus-type
solutions are interpreted as marginal bound states of these ``separatrix
walls''. All flat domain wall solutions, which are given exactly for any
$\lambda$, are shown to be supersymmetric for some superpotential $W$,
determined by the solution.
