  We study a stochastic Nonlinear Schroedinger Equation (NLSE), with additive
white Gaussian noise, by means of the Nonlinear Fourier Transform (NFT). In
particular, we focus on the propagation of discrete eigenvalues along a
focusing fiber. Since the stochastic NLSE is not exactly integrable by means of
the NFT, then we use a perturbation approach, where we assume that the
signal-to-noise ratio is high. The zeroth-order perturbation leads to the
deterministic NLSE while the first-order perturbation allows to describe the
statistics of the discrete eigenvalues. This is important to understand the
properties of the channel for recently devised optical transmission techniques,
where the information is encoded in the nonlinear Fourier spectrum.
