  A space-time crystal has recently been observed in a superfluid Bose gas.
Here we construct a variational model that allows us to describe from first
principles the coupling between the radial breathing mode and the higher-order
axial modes that underlies the observation of the space-time crystal. By
comparing with numerical simulations we verify the validity of our variational
Ansatz. From the model we determine the requirements for the observation of the
space-time crystal and the Ising-like nature of the symmetry breaking involved.
Also, we find the onset and growth rate of the space-time crystal, which can be
compared to experiments.
