Abstract

We analytically describe the effective evolution of a pulse (nonreturn-to-zero or return-to-zero) that propagates under the influence of a mean-zero dispersion map, nonlinearity, loss, and periodic amplification. On averaging, the governing equation is reduced to a set of coupled, nonlinear diffusion equations that describe the evolution of the pulse amplitude and phase and which capture the long-term interaction of dispersion and nonlinearity. The averaged equations are shown to be in good agreement with the full evolution until a predicted wave-breaking behavior is observed in the full equations.

© 1997 Optical Society of America

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