It is presented a theory of a chirped breathing soliton propagation in the dispersion-managed fiber links. It is shown that a fast (over one period) dynamics of the pulse is governed by a system of two ordinary differential equations for the pulse width and chirp. Dispersion-managed pulses can propagate stably not only in the region of the anomalous average dispersion, but also with zero average path dispersion and even in the region of normal residual dispersion. Under some assumptions a slow (average) evolution of the central part of the peak can be approximated by the nonlinear Schrodinger equation (NLSE) with additional parabolic potential. If an effective parabolic potential is of a nontrapping type, the radiation is tunneling from the main peak. Asymptotic dispersion-managed (DM) soliton forming in such systems presents a central peak surrounded by oscillatory tails. It is demonstrated that using additional gratings after compensation cell it is possible to produce a pulse with strong confinement. Such pulse has all attractive features of the quasi-soliton suggested by Kumar and Hasegawa, but can be produced with simple dispersion management. Fast decaying tail and a rotation of the relative phase (due to chirp) between neighboring solitons reduce soliton interaction and allow for denser information packing.
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