Multiple-scale averaging is applied to the nonlinear Schrödinger equation with rapidly varying coefficients, the results are used to analyze pulse propagation in an optical fiber when a periodic dispersion map is employed. The effects of fiber loss and repeated amplification are taken into account by use of a coordinate transformation to relate the pulse dynamics in lossy fibers to that in equivalent lossless fibers. Second-order averaaing leads to a general evolution equation that is applicable to both return-to-zero (soliton) and non-return-tozero encoding schemes. The resulting equation is then applied to the specific case of solitons, and an asymptotic theory for the pulse dynamics is developed. Based upon the theory, a simple and effective design of two-step dispersion maps that are advantageous for wavelength-division-multiplexed soliton transmission is proposed. The use of these specifically designed dispersion maps allows simultaneous minimization of dispersive radiation in several different channels.
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