Equations of a semiclassical model of superradiant Rayleigh scattering of high-intensity short light pulses from a Bose-Einstein condensate of dilute atomic gases are solved numerically taking into account the excitation of atoms by coherent Rayleigh radiation and their recoil in the backward direction. The evolution of the populations of coherent atomic states with a particular momentum is studied, and the pulse shape and the structure of the spectrum of such scattering are found in relation to the laser beam intensity and the recoil kinetic energy of atoms.
The superradiant Rayleigh scattering of high-intensity light pulses by the Bose-Einstein condensate of rubidium vapor is studied using the model proposed earlier. It is demonstrated that four states with a certain momentum are occupied under the experimental conditions (two states correspond to the forward recoil and two others correspond to the backward recoil). Condensate pulsations between the zero-momentum state and the above states are detected and studied. The corresponding shape of the coherent Rayleigh pulse is found.