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

Black brane solutions and their solitonic extremal limit in Einstein-scalar gravity