Transient behavior of the amplification of the Stokes field by thermal Rayleigh and Brillouin effects

We derive analytical solution for a signal field amplified by stimulated Rayleigh and Brillouin effects. The presence of light absorption is taken into account. The solution describes the transient behavior at all frequency differences between the pump and the signal waves. The validity is demonstrated for the simple case of no absorption, and the particular time behavior at $\omega =0\mathrm{}$ is stressed.