Abstract In this paper, the generalized second-order nonlinear Schrödinger equation with light-wave promulgation in an optical fiber, is studied for optical soliton solutions. Three analytical methods such as the exp ( − ϕ ( χ ) ) $\mathrm{exp}\left(-\phi \left(\chi \right)\right)$ -expansion method, the G′/G 2-expansion method and the first integral methods are used to extract dark, singular, periodic, dark-singular combo optical solitons for the proposed model. These solitons appear with constraint conditions on their parameters and they are also presented. These three strategic schemes have made this retrieval successful. The given model is also studied for modulation instability on the basis of linear stability analysis. A dispersion relation is obtained between wave number and frequency.

中文翻译：

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光纤中广义二阶非线性薛定谔方程的光孤子和稳定性分析

摘要 本文研究了光纤中具有光波传播的广义二阶非线性薛定谔方程的光孤子解。exp ( − ϕ ( χ ) ) $\mathrm{exp}\left(-\phi \left(\chi \right)\right)$ -展开法、G′/G 2-展开法等三种解析方法方法和第一积分方法用于为所提出的模型提取暗、奇异、周期、暗-奇异组合光学孤子。这些孤子在其参数上带有约束条件，并且它们也被呈现出来。这三个战略方案使这次检索取得了成功。在线性稳定性分析的基础上，还研究了给定模型的调制不稳定性。获得波数和频率之间的色散关系。