ABSTRACT We study the propagation of ultrashort pulses of width around sub-10 femtosecond in an inhomogeneous highly nonlinear single-mode fibre within the framework of a generalized higher-order nonlinear Schrödinger equation with derivative non-Kerr nonlinear terms and spatially inhomogeneous coefficients. Additional effects to the cubic model include the distributed third-order dispersion, self-steepening, self-frequency shift due to stimulated Raman scattering, quintic nonKerr nonlinearity, derivative non-Kerr nonlinear terms, and gain or loss. The exact self-similar brightand dark-solitary-wave solutions of the governing equation are derived via a transformation connected with the constant-coefficient higher-order nonlinear Schrödinger equation with non-Kerr nonlinearity. The constraint relations among the optical fibre parameters for the existence of these self-similar structures are also discussed. Based on these exact solutions, we investigate the dynamical behaviours of self-similar localized pulses in a periodic distributed fibre system for different parameters.

中文翻译：

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非均匀高度非线性光纤放大器中自相似亚 10-fs 脉冲的动力学

摘要 我们在具有导数非克尔非线性项和空间非均匀系数的广义高阶非线性薛定谔方程的框架内研究了宽度在 10 飞秒左右的超短脉冲在非均匀高度非线性单模光纤中的传播。三次模型的其他影响包括分布式三阶色散、自陡峭、由于受激拉曼散射引起的自频移、五次非克尔非线性、导数非克尔非线性项以及增益或损失。控制方程的精确自相似明暗孤立波解是通过与具有非克尔非线性的常系数高阶非线性薛定谔方程相关联的变换导出的。还讨论了存在这些自相似结构的光纤参数之间的约束关系。基于这些精确解，我们研究了周期性分布式光纤系统中不同参数的自相似局部脉冲的动力学行为。