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 pro
cedure. 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.
High amplification events (HAEs) are common phenomena in extragalactic gravitational lens systems (GLSs), where the multiple images of a distant quasar are observed through a foreground galaxy. There is a considerable brightness magnification in one
of the quasar images during HAE. Grieger, Kayser, and Refsdal (1988) proposed to use HAEs to study the central regions of quasars in GLSs. In this paper, we consider some problems concerning the identification of different source types on the basis of the HAE observations. We compare the results of light curve simulations to estimate a feasibility to distinguish different source models in GLSs. Analytic approximation methods yielding solutions of the lens equation in a vicinity of fold caustic crossing events are presented. The results are used to obtain amplification factors, which the higher-order corrections for the Gaussian, power-law, and limb-darkening models of a source take into account.
