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 this we have used the conservation and Einstein equations to describe the evolution of gravitationally coupled inhomogeneities of dark matter, dark energy and radiation from the linear stage in the early Universe to the non-linear stage at the current epoch. A simple method of 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 the halo of cluster (k = 2 Mpc(-1)) and supercluster scales (k = 0.2 Mpc(-1)) and show that a quintessential scalar field dark energy with a low value of effective speed of sound c(s) < 0.1 can have a notable impact on the formation of large-scale structures in the expanding Universe.