  The dynamics of a two-dimensional Bose-Einstein condensate in a presence of
quantum fluctuations is studied. The properties of localized density
distributions, quantum droplets (QDs), are analyzed by means of the variational
approach. It is demonstrated that the super-Gaussian function gives a good
approximation for profiles of fundamental QDs and droplets with non-zero
vorticity. The dynamical equations for parameters of QDs are obtained. Fixed
points of these equations determine the parameters of stationary QDs. The
period of small oscillations of QDs near the stationary state is estimated. It
is obtained that periodic modulations of the strength of quantum fluctuations
can actuate different processes, including resonance oscillations of the QD
parameters, an emission of waves and a splitting of QDs into smaller droplets.
