Based on the Maxwell equations the general and complete expression of the equation governing the nonlinear propagation in optical fibers is obtained. The energy and momentum equations for the soliton in consideration of attenuation and high-order dispersion are also given, from which a general analytical solution is derived for small-loss cases. A numerical study is carried out on the effect of various factors on the propagation of solitons, and some new and important results are obtained.
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