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We apply the potential reconstruction approach to generate a series ofasymptotically AdS (aAdS) black hole solutions, with a self-interacting bulkscalar field. Based on the method, we reproduce the pure AdS solution as aconsistency check and we also generate a simple analytic 5D black holesolution. We then study various aspects of this solution, such as temperature,entropy density and conserved charges. Furthermore, we study the hydrodynamicsof this black hole solution in the framework of fluid/gravity duality, e.g. theratio of the shear viscosity to the entropy density. In a degenerate case ofthe 5D black hole solution, we find that the c function decreases monotonicallyfrom UV to IR as expected. Finally, we investigate the stability of thedegenerate solution by studying the bosonic functional energy of the gravityand the Witten-Nester energy $E_{WN}$. We confirm that the degenerate solutionis a BPS domain wall solution. The corresponding superpotential and thesolution of the killing spinor equation are found explicitly.

Hydrodynamics of a 5D Einstein-dilaton black hole solution and the corresponding BPS state