Recent progress in optical fibers is impressive, while nonlinear Schrödinger-type models are seen in fiber optics and other fields (such as ferromagnetism, plasma physics, Bose–Einstein condensation and oceanography). Hereby, our symbolic computation on a three-coupled variable-coefficient nonlinear Schrödinger system is performed, for the picosecond-pulse attenuation/amplification in a multicomponent inhomogeneous optical fiber with diverse polarizations/frequencies. For the slowly-varying envelopes of optical modes, we obtain a similarity reduction, an auto-Bäcklund transformation and some analytic solutions, which rely on the optical-fiber variable coefficients, i.e., the fiber loss/gain, nonlinearity and group velocity dispersion. Relevant variable-coefficient constraints are presented. Our results might be of some use in the construction of logic gates, optical computing, soliton switching, design of fiber directional couplers, quantum information processing, soliton amplification in the wavelength division multiplexing systems, solitonic studies in the all-optical devices and birefringence fiber systems.

光纤的最新进展令人印象深刻，而非线性Schrödinger型模型在光纤和其他领域（例如铁磁性，等离子体物理，玻色-爱因斯坦凝聚和海洋学）中得到了应用。据此，我们对三耦合可变系数非线性Schrödinger系统进行了符号计算，以对具有不同偏振/频率的多分量非均匀光纤中的皮秒脉冲进行衰减/放大。对于光学模式的缓慢变化的包络线，我们获得了相似度降低，自动巴克伦变换和一些解析解，这些解析解依赖于光纤可变系数，即光纤损耗/增益，非线性和群速度色散。提出了相关的变量系数约束。