布朗运动对三元非线性施罗丁格方程的光学单元解决方案的影响
Muhammad Zafarullah Baber1, Tahir Shahzad2, Wael W Mohammed3
1Department of Mathematics and Statistics, The University of Lahore, Sargodha campus, Pakistan.
Scientific reports
|July 16, 2025
概括
本研究探讨了与布朗运动的非线性施罗丁格方程的光学单子解决方案. 它可视化各种单体类型的噪声效应,通过模拟证实稳定性.
科学领域:
- 非线性光学是一种非线性光学.
- 数学物理学的数学物理.
- 光学通信是指光学通信的应用.
背景情况:
- 在双折光纤中光脉冲的传播是通过合的非线性施罗丁格方程建模的.
- 这些方程解释了两极化模式和三波混合效应之间的相互作用,例如交叉相调制 (XPM) 和四波混合 (FWM).
研究的目的:
- 在布朗运动下研究三元非线性随机施罗丁格方程的精确光学单子解.
- 分析噪声对不同类型光学单子及其稳定性的影响.
主要方法:
- 采用了一般化的里卡蒂方程映射方法来构建暗,单一,组合和单一波解决方案.
- 修改后的辅助方程方法被用来证实所得到的解决方案的稳定性,产生了超标,三角形和理性单元.
- 使用Mathematica 11.1的模拟可视化了3D,2D和轮图中的单元解决方案上的噪声效应.
主要成果:
- 对于各种光学单子 (暗,单,组合,单,超标,三角,理性) 的精确解决方案得到了成功的推导.
- 布朗运动 (噪声) 对这些光学单子的行为和稳定性的影响通过计算模拟有效地可视化.
- 通过两种不同的数学方法证实了衍生解决方案的稳定性.
结论:
- 该研究成功地推导和分析了在随机噪声下复杂的非线性系统的各种光学单元解决方案.
- 这些发现突出了噪声对单子传播和双折光纤稳定性的重大影响.
- 采用的方法为研究具有随机影响的光学系统中的非线性现象提供了强大的框架.
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