  We present the Gross-Pitaevskii equation for Bose-Einstein condensates (BECs)
possessing the electric dipole and the electric quadrupole moments in a
non-integral form. These equations are coupled with the Maxwell equations. The
model under consideration includes the dipole-dipole, the dipole-quadrupole,
and the quadrupole-quadrupole interactions in terms of the electric field
created by the dipoles and quadrupoles. We apply this model to obtain the
Bogoliubov spectrum for three dimensional BECs with a repulsive short-range
interaction. We obtain an extra term in the Bogoliubov spectrum in compare with
the dipolar BECs. We show that the quadrupole-quadrupole interaction gives a
positive contribution in the Bogoliubov spectrum. Hence this spectrum is
stable.
