We show, through second order moment theory, the existence of a new regime of self-similar chirped-solitary wave in an appropriately dispersion-profiled fibre. This study completes the concept of quasi-solitons introduced by Kumar and Hasegawa. Theory reveals the existence of an invariant relation respected by quasi-solitons. This invariant relation can be fully recovered by the usual variational approach of the non-linear Schroedinger equation (NLS) and it can be used to study non-linear pulse propagation in constant dispersion optical fibers and ultimately for dispersion management. The work has been carried out for the lossless as well as for the lossy case.
We derive approximate expressions to predict the chirp and peak power of a pulse propagating through a given
dispersion map with lumped amplifiers. We use second-order moments to derive expressions for the evolution of the
root-mean-square (RMS) width and chirp parameters within one period of the map. Numerical simulations confirm the
accuracy of the analytical model.