  We consider an extended Korteweg-de Vries (eKdV) equation, the usual
Korteweg-de Vries equation with inclusion of an additional cubic nonlinearity.
We investigate the statistical behaviour of flat-top solitary waves described
by an eKdV equation in the presence of weak dissipative disorder in the linear
growth/damping term. With the weak disorder in the system, the amplitude of
solitary wave randomly fluctuates during evolution. We demonstrate numerically
that the probability density function of a solitary wave parameter $\kappa$
which characterizes the soliton amplitude exhibits loglognormal divergence near
the maximum possible $\kappa$ value.
