  Using variational and numerical solutions of the mean-field Gross-Pitaevskii
equation we show that a bright soliton can be stabilized in a trapless
three-dimensional attractive Bose-Einstein condensate (BEC) by a rapid periodic
temporal modulation of scattering length alone by using a Feshbach resonance.
This scheme also stabilizes a rotating vortex soliton in two dimensions. Apart
from possible experimental application in BEC, the present study suggests that
the spatiotemporal solitons of nonlinear optics in three dimensions can also be
stabilized in a layered Kerr medium with sign-changing nonlinearity along the
propagation direction.
