  We present fully dynamical solutions to Einstein-scalar theory in
asymptotically Anti-de-Sitter spacetime with a scalar potential containing
particularly rich physics. Depending on one parameter in the potential we find
an especially interesting regime, which exhibits a thermodynamically stable,
but dynamically unstable black brane, even at zero momentum. We show this using
the non-linear dynamics, and give a clear interpretation in terms of the
spectrum of linearized perturbations. Our results translate directly to their
dual strongly coupled non-conformal field theories.
