  Collective excitations in graphene monolayer are studied. Equations
describing collective properties of electrons in graphene are obtained. The
basic ideas of the method of many-particle quantum hydrodynamics are used for
the derivation. As starting point of the derivation we use the Dirac equation
for massless electrons which is usually used for description of electrons in
graphene [D. E. Sheehy and J. Schmalian, Phys. Rev. Lett. 99, 226803 (2007)],
where the Coulomb interaction is taken into account. We study dispersion
properties of collective excitations by means derived here graphene quantum
hydrodynamics equations (GQHD). We consider graphene in the external magnetic
field which directed at an angle to the graphene sample. We do it in a linear
approximation of the GQHD equations. We observe that the magnetic field
directed perpendicular to the graphene plane had no influence on dispersion of
the collective excitations. For the magnetic field directed at an angle to the
graphene we obtain dependence of wave dispersion on system parameters: strength
of magnetic field, wave vector, direction of wave propagation relatively to the
magnetic field.
