  We review some results of our paper arXiv:1602.05171v2 on the "nonlinear
quasifree approximation" to the many-body Schr\"odinger dynamics of Bose gases.
In that paper, we derive, with the help of this approximation, the
time-dependent Hartree-Fock-Bogoliubov (HFB) equations, providing an
approximate description of the dynamics of quantum fluctuations around a
Bose-Einstein condensate and study properties of these equations.
