First-order nonlinear perturbations of several fiber spans may be summed up linearly to yield the total nonlinear response of a group of spans, if nonlinear effects are neglected beyond the first order. Such linear additivity of first-order nonlinear perturbations about the nonlinear coefficients enables nonlinear compensations between one span with stronger nonlinearity and a group of spans with weaker nonlinearity, provided that there is a scaled translation symmetry between the strongly and the weakly nonlinear spans, and the dispersion of each span is properly managed. Excellent nonlinear compensations are achieved both in systems with an optical phase conjugator in the middle and in systems without.
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Qi et al. (2006) studied this question.