Path-averaged chirped optical soliton in dispersion-managed fiber communication lines

We present a comprehensive path-average theory of dispersion-managed (DM) optical pulse. Applying complete basis of the chirped Gauss-Hermite orthogonal functions, we derive a path-average propagation equation in the time domain and present an analytical description of the breathing dynamics of the chirped DM soliton. This theory describes both self-similar evolution of the central, energy-containing core and accompanying nonstationary oscillations of the far-field tails of an optical pulse propagating in a fiber line with an arbitrary dispersion map. In the case of a strong dispersion management the DM soliton is well described by a few modes in this expansion, justifying the use of a Gaussian trial function in the previously developed variational approach. Suggested expansion in the basis of chirped Gauss-Hermite functions presents a regular way to describe soliton properties for arbitrary dispersion map and to account for the effect of practical perturbations (filters, gratings, noise an so on) on the dynamics of the ideal DM soliton. We also present path-averaged propagation model in the spectral domain that could be useful for multichannel transmission applications. Theoretical results are verified by numerical simulations.