  The existence regimes and dynamics of soliton molecules in dispersion-managed
(DM) optical fibers have been studied. Initially we develop a variational
approximation (VA) for description of periodic dynamics of a soliton molecule
within each unit cell of the dispersion map. The obtained system of coupled
equations for the pulse width and chirp allows to find the parameters of DM
soliton molecules for the given dispersion map and pulse energy. Then by means
of a scaling transformation and averaging procedure we reduce the original
nonlinear Schr\"odinger equation (NLSE) with piecewise-constant periodic
dispersion to its counterpart with constant coefficients and additional
parabolic potential. The obtained averaged NLSE with expulsive potential can
explain the essential features of solitons and soliton molecules in DM fibers
related to their energy loss during propagation. Also, the model of averaged
NLSE predicts the instability of the temporal position of the soliton, which
may lead to difficulty in holding the pulse in the middle of its time slot. All
numerical simulations are performed using the parameters of the existing DM
fiber setup, and illustrated via pertinent examples.
