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.