  We develop a novel model of the magnetized spin-1 Bose-Einstein condensate
(BEC) of neutral atoms, using the method of many-particle quantum hydrodynamic
(QHD) and propose an original derivation of the system of continual equations.
We consider bosons with a spin-spin interaction and a short range interaction
in the first order in the interaction radius, on the of basis of the
self-consistent field approximation of the QHD equations. We demonstrate that
the dynamics of the fluid velocity and magnetization is determined by a
nontrivial modification of the Euler and Landau-Lifshitz equation, and show
that a nontrivial modification of the spin density evolution equation contains
the spin torque effect that arises from the self-interactions between spins of
the bosons. The properties of the dispersion spectrum of collective excitations
are described. We obtain the new contribution of the self-interaction of spins
in the spin wave spectrum together with the influence of an external magnetic
field and spin-spin interactions between polarized particles. The anisotropic
spin wave instability is predicted.
