  The quantum statistics of damped optical solitons is studied using
cumulant-expansion techniques. The effect of absorption is described in terms
of ordinary Markovian relaxation theory, by coupling the optical field to a
continuum of reservoir modes. After introduction of local bosonic field
operators and spatial discretization pseudo-Fokker-Planck equations for
multidimensional s-parameterized phase-space functions are derived. These
partial differential equations are equivalent to an infinite set of ordinary
differential equations for the cumulants of the phase-space functions.
Introducing an appropriate truncation condition, the resulting finite set of
cumulant evolution equations can be solved numerically. Solutions are presented
in Gaussian approximation and the quantum noise is calculated, with special
emphasis on squeezing and the recently measured spectral photon-number
correlations [Spaelter et al., Phys. Rev. Lett. 81, 786 (1998)].
