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采用半经典理论，建立了Ｅｒ￣（３＋）掺杂光纤中孤子的传输放大方程。该方程考虑泵浦激发态吸收，故适用于０．５－１．４９μｍ波长范围的所有泵浦情况。同时，该方程适用于任意折射率分布光纤，任意泵浦和信号光波模式、任意掺杂形状、均匀加宽和非均匀加宽、集总放大和分布放大，为深入研究Ｅｒ￣（３＋）渗杂光纤孤子放大特性、优化掺杂光纤设计提供了必须的基本分析方程。
The semi-classical theory is used to establish the propagation amplification equation of soliton in Er¯ (3+) doped fiber. The equation takes into account the pumping excited state absorption and is therefore suitable for all pump conditions in the 0.5-1.49 μm wavelength range. At the same time, this equation is suitable for any refractive index distribution optical fiber, arbitrary pumping and signal light wave modes, arbitrary doping shape, uniform widening and non-uniform widening, lumped amplification and distributed amplification. In order to further study Er¯ (3+) The optical fiber soliton amplification characteristics, optimization of doped optical fiber design provides the necessary basic analytical equations.