  Faraday and resonant density waves emerge in Bose-Einstein condensates as a
result of harmonic driving of the system. They represent nonlinear excitations
and are generated due to the interaction-induced coupling of collective
oscillation modes and the existence of parametric resonances. Using a
mean-field variational and a full numerical approach, we studied density waves
in dipolar condensates at zero temperature, where breaking of the symmetry due
to anisotropy of the dipole-dipole interaction (DDI) plays an important role.
We derived variational equations of motion for the dynamics of a driven dipolar
system and identify the most unstable modes that correspond to the Faraday and
resonant waves. Based on this, we derived the analytical expressions for
spatial periods of both types of density waves as functions of the contact and
the DDI strength. We compared the obtained variational results with the results
of extensive numerical simulations that solve the dipolar Gross-Pitaevskii
equation in 3D, and found a very good agreement.
