In this article, we investigate the optical soiltons and other solutions to Kudryashov’s equation (KE) that describe the propagation of pulses in optical fibers with four non-linear terms. Non-linear Schrodinger equation with a non-linearity depending on an arbitrary power is the base of this equation. Different kinds of solutions like optical dark, bright, singular soliton solutions, hyperbolic, rational, trigonometric function, as well as Jacobi elliptic function (JEF) solutions are obtained. The strategy that is used to extract the dynamics of soliton is known as [Formula: see text]-model expansion method. Singular periodic wave solutions are recovered and the constraint conditions, which provide the guarantee to the soliton solutions are also reported. Moreover, modulation instability (MI) analysis of the governing equation is also discussed. By selecting the appropriate choices of the parameters, 3D, 2D, and contour graphs and gain spectrum for the MI analysis are sketched. The obtained outcomes show that the applied method is concise, direct, elementary, and can be imposed in more complex phenomena with the assistant of symbolic computations.

中文翻译：

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四非线性项描述光纤中传播脉冲的广义模型调制不稳定性分析及光孤子

在本文中，我们研究了 Kudryashov 方程 (KE) 的光学土壤和其他解，该方程描述了具有四个非线性项的光纤中脉冲的传播。非线性薛定谔方程具有取决于任意幂的非线性是该方程的基础。得到了不同种类的解，如光学暗解、亮解、奇异孤子解、双曲解、有理解、三角函数解以及雅可比椭圆函数（JEF）解。用于提取孤子动力学的策略称为[公式：见正文]-模型扩展方法。恢复了奇异周期波解，并给出了为孤子解提供保证的约束条件。此外，还讨论了控制方程的调制不稳定性（MI）分析。通过选择适当的参数选择，绘制用于 MI 分析的 3D、2D 和等高线图和增益谱。所得结果表明，所应用的方法简洁、直接、基本，可以在符号计算的辅助下应用于更复杂的现象。