  We describe recent development of quantum hydrodynamics for ultracold Bose
particle studying and consider different kinds of interactions. The method of
derivation of equations describing the evolution of the neutral Bose particle
system at low temperatures is described. Despite the fact that we consider the
neutral particles we account the short-range interaction between particles. We
consider the particles in the Bose-Einstein condensate (BEC) state. This method
is called the method of quantum hydrodynamics, because natural for of the
quantum mechanics rewritten in terms of material fields of observable
quantities in three dimensional space is the set of equations, which look like
the hydrodynamics equations. It can be shown that from the quantum
hydrodynamics equations can be derived macroscopic non-linear Schrodinger
equation. Most famous non-linear Schrodinger equation is the Gross-Pitaevskii
(GP) equation, which contains nonlinearity of the third degree. There are
generalizations of the GP equation. New term appears in the GP equation at
account of the three-particle interaction. This term contains nonlinearity of
the fifth degree. At more detailed account of the two particle interaction we
come to the nonlocal non-linear Schrodinger equation. This equation contains
spatial derivatives of the order parameter in the non-linear terms caused by
the interaction. In this terminology the GP equation corresponds to the first
order by the interaction radius. For the BEC of the neutral particles with
anisotropic long-range dipole-dipole interaction the generalization of the GP
equation was also suggested. Detailed analyses of the applicability conditions
shows that this equation valid for the system of dipoles parallel to each
other, which do not change their direction, and where the dipole-dipole
interaction interferences translational motion of particles.
