In this research article, our aim is to construct new optical soliton solutions for nonlinear complex Ginzburg–Landau equation with the help of modified mathematical technique. In this work, we studied both laws of nonlinearity (Kerr and power laws). The obtained solutions represent dark and bright solitons, singular and combined bright-dark solitons, traveling wave, and periodic solitary wave. The determined solutions provide help in the development of optical fibers, soliton dynamics, and nonlinear optics. The constructed solitonic solutions prove that the applicable technique is more reliable, efficient, fruitful and powerful to investigate higher order complex nonlinear partial differential equations (PDEs) involved in mathematical physics, quantum plasma, geophysics, mechanics, fiber optics, field of engineering, and many other kinds of applied sciences.

中文翻译：

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具有非线性克尔定律介质的非线性复 Ginzburg-Landau 动力学方程的光孤子解

在这篇研究文章中，我们的目标是借助改进的数学技术为非线性复杂的 Ginzburg-Landau 方程构建新的光学孤子解。在这项工作中，我们研究了非线性定律（克尔定律和幂定律）。得到的解代表暗和亮孤子、奇异和组合亮暗孤子、行波和周期性孤立波。确定的解决方案为光纤、孤子动力学和非线性光学的开发提供了帮助。所构建的孤子解证明了该技术在研究数学物理、量子等离子体、地球物理、力学、光纤光学、工程领域、