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in a supersymmetric theory. In addition, it has been shown that one may consider a Big Bang model of the Universe in the presence of dilaton field and presented Liouville-type potential which can mimic the matter (including dark matter) and dark energy. This model predict age of the Universe, transition redshift, Big Bang nucleosynthesis and evolution of dark energy agree with current observations [25]. Also, this type of potential can be obtained when a higher dimensional theory is compactified to four dimensions, including various super gravity models [26] (see also [27] for a recent discussion of these aspects). In particular, for special values of coupling constant, α , this potential reduce to the supersymmetry potential of Gates and Zwiebach in string theory [26]. 

For later convenience we redefine Λ = − n ( n − 1) / 2 l $^{2}$, where l is the AdS radius of spacetime. It is clear the cosmological constant is coupled to the dilaton in a very nontrivial way. In the absence of the dilaton field action (1) reduces to the action of Einstein-Maxwell gravity with cosmological constant. Considering this type of dilaton potential, one can extract successfully the AdS solutions of Einstein–Maxwell-dilaton gravity [28, 29]. 

The rest of this paper is outlined as follows. In the next section, we consider the field equations of Einstein-Maxwell-dilaton gravity and present the ( n +1)-dimensional topological AdS black brane solutions and investigate their properties. In section III, we obtain the conserved and thermodynamic quantities of the solutions and verify the validity of the first law of black brane thermodynamics. We perform a stability analysis in the canonical ensemble and disclose the effect of the dilaton field on the thermal stability of the solutions in section IV. Conclusions are drawn in the last section. 

## II. FIELD EQUATIONS AND SOLUTIONS 

Varying action (1) with respect to the metric tensor g$_{µν}$ , the dilaton field Φ and the electromagnetic potential A$_{µ}$ , the equations of motion are obtained as 

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