Abstract

We investigate the behavior of optical solitons within a nonlinear medium characterized by temporally varying second-order dispersion, cubic–quintic–septimal nonlinearities, and linear gain or loss. Our analysis yields analytical solutions for both bright and dark nonautonomous solitons governed by the generalized cubic–quintic–septimal nonlinear Schrödinger’s equation with time-dependent coefficients. These soliton solutions exhibit characteristics, including distributed parameters affecting their amplitude, position, and phase, offering effective control over their evolution. Through examination of different material parameters, we observe features in the evolution of these soliton structures, demonstrating the influence of system parameter modulation. Notably, our findings highlight the potential for dynamic control of soliton behavior through adjustments of time-modulated group velocity dispersion and gain or loss parameters.

中文翻译：

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时间调制三次-五次-隔数非线性介质中非自主孤子的传播动力学

摘要

我们研究了非线性介质中光孤子的行为，其特征是随时间变化的二阶色散、三次-五次-隔数非线性以及线性增益或损耗。我们的分析给出了亮和暗非自主孤子的解析解，这些孤子受广义三次-五次-七次非线性薛定谔方程与时间相关系数的控制。这些孤子解决方案表现出一些特性，包括影响其幅度、位置和相位的分布参数，从而对其演化提供有效控制。通过检查不同的材料参数，我们观察了这些孤子结构演化的特征，证明了系统参数调制的影响。值得注意的是，我们的研究结果强调了通过调整时间调制群速度色散和增益或损耗参数来动态控制孤子行为的潜力。