Average dynamics of the optical soliton in communication lines with dispersion management: Analytical results

Applying asymptotic methods to a previously derived system of ordinary differential equations, we present an analytical description of the slow (average) dynamics of self-similar breathing pulses propagating in fiber links with dispersion management. We derive asymptotic averaged quantities (adiabatic invariants) that characterize the stable pulse propagation. In a particular, but practically important, case when the dispersion compensation period is much larger than the amplification distance we have found analytically the fixed points corresponding to the dispersion-managed solitons.