  The truncated Wigner approximation is an established approach that describes
the dynamics of weakly interacting Bose gases beyond the mean-field level.
Although it allows a quantum field to be expressed by a stochastic c-number
field, the simulation of the time evolution is still very demanding for most
applications. Here, we develop a numerically inexpensive approximation by
decomposing the c-number field into a variational ansatz function and a
residual field. The dynamics of the ansatz function is described by a tractable
set of coupled ordinary stochastic differential equations for the respective
variational parameters. We investigate the non-equilibrium dynamics of a
three-dimensional Bose gas in a one-dimensional optical lattice with a
transverse isotropic harmonic confinement and neglect the influence of the
residual field. The accuracy and computational inexpensiveness of our method
are demonstrated by comparing its predictions to experimental data.
