The pump wave reflected from the overdense plasma may play an important role in the dynamics of stimulated Brillouin scattering. The particular case of Double Stimulated Brillouin Scattering (DSBS) suggested by Zozulya, Silin, & Tikhonchuk [Sov. Phys. JETP 59, 756 (1984)] is studied here in detail. In DSBS the incident pump wave and the reflected pump wave scatter from a common ion acoustic wave. Some steady state properties of DSBS are reviewed. The analysis of DSBS dynamics is based on a series of ‘numerical experiments’.At small pump intensities the system asymptotically approaches a true steady state. When the intensity is increased the solution turns into a regular pulse train with intensity dependent period. Connections between the pulses and soliton-like solutions of a damped sine-Gordon equation are discussed.
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