The evolution of a randomly modulated sine-Gordon breather in a nonlinear m
edium is studied theoretically. The initial wave field is affected by multi
plicative noise. For breather amplitude and velocity, the probability distr
ibution function is determined by means of the inverse scattering transform
and the method of cumulants. The distributions are shown to be non-Gaussia
n. The mean and the most probable values of the breather amplitude and velo
city are calculated. (C) 2000 MAIK "Nauka/Interperiodica".