  Cascaded Brillouin scattering is increasingly becoming of interest in many
areas of pho- tonics (e.g. see [1] and [2]) and has been studied experimentally
by many groups. In gain assisted experiments for example up to nearly 800
distinct lines have been observed[3] while in passive cavities, mode locking of
a few Brillouin lines has recently been demonstrated[4]. We show that although
each pair of lines interact through the creation of an acoustic phonon the
resulting acoustic field nevertheless can be written as the sum of only two
waves (a forward and backward propagating wave). This new analysis results in a
set of strongly coupled amplitude equations for the fields that are derived
here for the first time in the context of optical fibres. More-over we show
that previous authors have mis- understood the nature of the acoustic field
resulting in incorrect sets of coupled equations.
