One-dimensional model of cosmological perturbations: direct integration in the Fourier space

We propose a method of calculation of the power spectrum of cosmological perturbations by means of a direct numerical integration of hydrodynamic equations in the Fourier space for a random ensemble of initial conditions with subsequent averaging procedure. This method can be an alternative to the cosmological N-body simulations. We test realizability of this method in case of one-dimensional motion of gravitating matter pressureless shells. In order to test the numerical simulations, we found an analytical solution which describes one-dimensional collapse of plane shells. The results are used to study a nonlinear interaction of different Fourier modes.