  We consider the backgrounds obtained by Abelian and non-Abelian T-duality
applied on $AdS_5\times S^5$. We study geodesics, calculate Penrose limits and
find the associated plane-wave geometries. We quantise the weakly coupled
type-IIA string theory on these backgrounds. We study the BMN sector, finding
operators that wrap the original quiver CFT. For the non-Abelian plane wave, we
find a 'flow' in the frequencies. We report some progress to understand this,
in terms of deconstruction of a higher dimensional field theory. We explore a
relation with the plane-wave limit of the Janus solution, which we also
provide.
