  The stability properties of a family of magnetic $AdS_{3}\times
\mathbb{R}^{2}$ solutions of D=5, SO(6) gauged SUGRA are investigated in more
detail. We construct an analogous family of magnetic $AdS_{2}\times
\mathbb{R}^{2}$ solutions of D=4, SO(8) gauged SUGRA, including a family of
supersymmetric solutions, and also investigate their stability. We construct
supersymmetric domain walls that interpolate between AdS_5 and an
$AdS_3\times\mathbb{R}^2$ solution and also between AdS_4 and an
$AdS_2\times\mathbb{R}^2$ solution which provide stable zero temperature ground
states for the corresponding dual CFTs. We also construct new families of
electric $AdS_{2}\times \mathbb{R}^{3}$ and $AdS_{2}\times \mathbb{R}^{2}$
solutions.
