The evolution of quasi-linear optical pulses in birefringent fibers, with strong dispersion-management, is studied analytically. The nonlinear terms of the Gabitov-Turitsyn equations (GTE) are analyzed asymptotically. The total spectral intensity, for a lossless system, is found to be an invariant of propagation, while for a lossy system it is dependent on the relative position of the amplifier in the dispersion map.