  Space folding techniques based on non-monotonic transforms lead to a new
class of cylindrical isotropic acoustic cloaks with a constant negative density
and a spatially varying negative bulk modulus. We consider an external cloak
consisting of a core with a positive definite density matrix and a positive
compressibility, and a shell with simultaneously negative density and
compressibility. Such a core-shell resonant system creates a virtual folded
region outside the shell. To handle such negative physical parameters in the
time-domain, a two-step strategy is used: (i) assuming resonant (Drude-type)
effective parameters in the frequency-domain; (ii) returning to the time-domain
by applying the formalism of the auxiliary fields. We numerically show that, at
the designed central frequency, scattering of a cylindrical pressure wave
incident upon a finite set of small rigid obstacles is drastically reduced
after a lapse of time, when they are placed in the close neighborhood of the
external cloak. However, at short times, the external cloak behaves rather like
a superscatterer: the cloak itself scatters more than the set of scatterers.
