A unified analytical description of the evolution of quasi-linear optical p
ulses and solitons in strongly dispersion-managed transmission systems is d
eveloped. Asymptotic analysis of the nonlocal equation that describes the a
veraged dynamics of a dispersion-managed system shows that the nonlinearity
decreases for large map strength s, as O(log s/s). The spectral intensity
is found to be an invariant of the propagation, which allows the phase shif
t to be computed. These findings provide a clear description of pulse propa
gation in the quasi-linear regime, which is characterized by much lower ene
rgies than those required for stable dispersion-managed soliton transmissio
n with the same dispersion map. (C) 2001 Optical Society of America.