  We consider, by means of the variational approximation (VA) and direct
numerical simulations of the Gross-Pitaevskii (GP) equation, the dynamics of 2D
and 3D condensates with a scattering length containing constant and
harmonically varying parts, which can be achieved with an ac magnetic field
tuned to the Feshbach resonance. For a rapid time modulation, we develop an
approach based on the direct averaging of the GP equation,without using the VA.
In the 2D case, both VA and direct simulations, as well as the averaging
method, reveal the existence of stable self-confined condensates without an
external trap, in agreement with qualitatively similar results recently
reported for spatial solitons in nonlinear optics. In the 3D case, the VA again
predicts the existence of a stable self-confined condensate without a trap. In
this case, direct simulations demonstrate that the stability is limited in
time, eventually switching into collapse, even though the constant part of the
scattering length is positive (but not too large). Thus a spatially uniform ac
magnetic field, resonantly tuned to control the scattering length, may play the
role of an effective trap confining the condensate, and sometimes causing its
collapse.
