This paper explores the optical solitons with Kerr laws nonlinearity for the complex Ginzburg–Landau equation with M-truncated and beta derivatives which describes solitons propagation. In this regard, two new methods, namely extended sub-equation and unified solver method, are used. From general, hyperbolic, and trigonometric functions, we obtain novel and general solitary solutions. All obtained solutions can be useful for a variety of important experiments in nuclear physics, fluid mechanics, and particle physics. Our results show the strength of the proposed technique for the determination of optical solitons of nonlinear evolution equations. The proposed methods can be applied for solving other fractional space–time NLEs arising in nonlinear optics.

本文探讨了具有描述孤子传播的 M 截断和 β 导数的复杂 Ginzburg-Landau 方程的具有克尔定律非线性的光学孤子。在这方面，使用了两种新方法，即扩展子方程和统一求解器方法。从一般函数、双曲线函数和三角函数中，我们获得了新颖和一般的孤立解。所有获得的解都可用于核物理学、流体力学和粒子物理学中的各种重要实验。我们的结果显示了所提出的用于确定非线性演化方程的光学孤子的技术的强度。所提出的方法可用于解决非线性光学中出现的其他分数时空 NLE。