Baber Muhammad Zafarullah, Ahmed Nauman, Yasin Muhammad Waqas, Iqbal Muhammad Sajid, Akgül Ali, Hassani Murad Khan, Jawaz Muhammad
Department of Mathematics and Statistics, The University of Lahore, Sargodha Campus, Pakistan.
Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.
Sci Rep. 2025 Mar 28;15(1):10707. doi: 10.1038/s41598-024-78912-3.
In this study, we consider the coupled nonlinear Schrödinger equation under the influence of the multiplicative time noise. The coupled nonlinear Schrödinger equation, which shows the complex envelope amplitudes of the two modulated weakly resonant waves in two polarisations and is used to describe the pulse propagation in high birefringence fibre, has several uses in optical fibres.query:Journal instruction requires a city for affiliations; however, these are missing in affiliation [6]. Please verify if the provided city are correct and amend if necessary. The underlying model is analyzed numerically and analytically as well. For the computational results, the proposed stochastic backward Euler scheme is developed and its consistency is derived in the mean square sense. For the linear stability analysis, Von-Neumann criteria is used, given proposed stochastic scheme is unconditionally stable. The exact optical soliton solutions are constructed with the help of the [Formula: see text]-model expansion technique, which provided us with the Jacobi elliptic function solutions that will explore optical solitons and solitary waves as well. The initial and boundary conditions are constructed for the numerical result by some optical soliton solutions. The 3D, 2D and corresponding contour plot are drawn for the different values of noise. Mainly, the comparison of results is shown graphically in 3D and line plots for some newly constructed solutions by selecting suitable parameters value.
在本研究中，我们考虑了乘性时间噪声影响下的耦合非线性薛定谔方程。该耦合非线性薛定谔方程描述了两个偏振方向上两个调制弱共振波的复包络振幅，用于描述高双折射光纤中的脉冲传播，在光纤中有多种用途。查询：期刊要求在单位信息中提供所在城市；然而，参考文献[6]中的单位信息缺少这些内容。请核实所提供的城市信息是否正确，如有必要请进行修改。同时对基础模型进行了数值分析和解析分析。对于计算结果，开发了所提出的随机向后欧拉格式，并在均方意义下推导了其一致性。对于线性稳定性分析，使用了冯·诺依曼准则，因为所提出的随机格式是无条件稳定的。借助[公式：见正文]模型展开技术构造了精确的光学孤子解，该技术为我们提供了雅可比椭圆函数解，这些解也将探索光学孤子和孤立波。通过一些光学孤子解构造了用于数值结果的初始条件和边界条件。针对不同的噪声值绘制了三维、二维及相应的等高线图。主要通过选择合适的参数值，以三维图和线图的形式直观展示了一些新构造解的结果比较。
