Dynamics of dark energy in collapsing halo of dark matter
  We investigate the non-linear evolution of spherical density and velocity
perturbations of dark matter and dark energy in the expanding Universe. For
that we have used the conservation and Einstein equations to describe the
evolution of gravitationally coupled inhomogeneities of dark matter, dark
energy and radiation from linear stage in the early Universe to the non-linear
one at the current epoch. The simple method of the numerical integration of the
system of non-linear differential equations for evolution of the central part
of halo is proposed. The results are presented for halo of cluster ($k=2$
Mpc$^{-1}$) and supercluster scales ($k=0.2$ Mpc$^{-1}$) and show that
quintessential scalar field dark energy with small value of effective speed of
sound $c_s<0.1$ can give noticeable impact on the formation of large scale
structures in the expanding Universe.
