  Recently an analytical model was presented that treats the nonlinear signal
distortion from the Kerr nonlinearity in optical transmission systems as
additive white Gaussian noise. This important model predicts the impact of the
Kerr nonlinearity in systems operating at a high symbol rate and where the
accumulated dispersion at the receiver is large. Starting from the suggested
model for the propagating signal, we here give an independent and different
calculation of the main result. The analysis is based on the Manakov equation
with attenuation included and a complete and detailed derivation is given using
a perturbation analysis. As in the case with the published model, in addition
to assuming that the input signal can be written on a specific form, two
further assumptions are necessary; the nonlinearity is weak and the
signal-noise interaction is neglected. The result is then found without any
further approximations.
