Rabie Wafaa B, Almotairi Eman S, Ahmed Hamdy M, Ali Mohammed H
Department of Mathematics, Faculty of Science, Luxor University, Taiba, Luxor, Egypt.
Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia.
Sci Rep. 2025 Aug 18;15(1):30165. doi: 10.1038/s41598-025-15978-7.
Stochastic optical solitons are a fascinating phenomenon in nonlinear optics where soliton-like behavior emerges in systems affected by stochastic noise. This study establishes a fundamental framework for stochastic wave propagation in birefringent fibers through the cubic-quintic-septic nonlinear Schrödinger equation (NLSE). Our modified extended mapping technique yields exact analytical solutions (bright, dark, and singular solitons, periodic structures, and Weierstrass elliptic waves) that explicitly incorporate multiplicative noise and birefringent coupling. We explore the influence of noise intensity on soliton stability and morphology through parameter analysis and visual simulations, revealing how stochastic fluctuations modify amplitude, phase, and localization. The visualized results in Figures 1-3 not only validate the analytical expressions but also provide intuitive insight into the role of noise in shaping wave evolution. These findings are crucial for the development of noise-tolerant optical soliton systems, especially in ultra-fast communication platforms, nonlinear fiber lasers, and integrated photonic circuits.
随机光学孤子是非线性光学中一种引人入胜的现象，在受随机噪声影响的系统中会出现类似孤子的行为。本研究通过立方-五次-七次非线性薛定谔方程（NLSE）建立了双折射光纤中随机波传播的基本框架。我们改进的扩展映射技术产生了精确的解析解（亮孤子、暗孤子和奇异孤子、周期结构以及魏尔斯特拉斯椭圆波），这些解明确地纳入了乘性噪声和双折射耦合。我们通过参数分析和可视化模拟探讨了噪声强度对孤子稳定性和形态的影响，揭示了随机涨落如何改变振幅、相位和局域化。图1 - 3中的可视化结果不仅验证了解析表达式，还直观地展示了噪声在塑造波演化过程中的作用。这些发现对于耐噪声光学孤子系统的发展至关重要，特别是在超快通信平台、非线性光纤激光器和集成光子电路中。
