The propagation of optical pulses is considered at the zero-dispersion wavelength of nonlinear dispersive fibers. Even in the absence of group-velocity (first-order) dispersion, higher-order dispersive effects in single-mode silica fibers are found to be strong enough to cause significant broadening and distortion of picosecond optical pulses for fiber lengths of 10--100 km. Using the parameters appropriate for a 1.55-\ensuremath{\mu}m dispersion-shifted single-mode fiber, we have studied the evolution of pulse shapes and pulse spectra along the fiber length for a wide range of initial pulse widths. For peak powers \ensuremath{\sim}10 mW, the dispersive and nonlinear effects are comparable for pulse widths \ensuremath{\sim}1 ps and their mutual interplay leads to new qualitative features in the pulse shape and spectrum that are largely independent of the input profile. The theoretical results are useful for an understanding of the higher-order dispersion and, at the same time, have implications for high-capacity, long-haul, optical communication systems.
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