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We discuss an analytical model that predicts the impact of the Kerr nonlinearity in optical communication systems when the signal spectrum is wide and the accumulated dispersion during propagation is large. A detailed derivation of this model is given for a generalized system by means of a perturbation analysis of the Manakov equation with attenuation, gain, and third order dispersion included. As in the case with previous studies, three simplifying assumptions are necessary. These are that (i) the nonlinearity is weak, (ii) the input signal is of a given specific form, and (iii) the signal-noise interaction can be neglected. Under these assumptions, the result is found exactly. We also discuss the accuracy of the analytical result and show that third order dispersion has a small impact in practice.