  We investigate static, planar, solutions of Einstein-scalar gravity admitting
an anti-de Sitter (AdS) vacuum. When the squared mass of the scalar field is
positive and the scalar potential can be derived from a superpotential, minimum
energy theorems indicate the existence of a scalar soliton. On the other hand,
for these models, no-hair theorems forbid the existence of hairy black brane
solutions with AdS asymptotics. By considering a specific example (an exact
integrable model which has the form of a Toda molecule) and by deriving
explicit exact solution, we show that these models allow for hairy black brane
solutions with non-AdS domain wall asymptotics, whose extremal limit is a
scalar soliton. The soliton smoothly interpolates between a non-AdS domain wall
solution at $r=\infty$ and an AdS solution near $r=0$.
