Fan Wenjie, Liang Ying, Han Tianyong
College of Computer Science, Chengdu University, Chengdu, 610106, China.
Interior Layout optimization and Security Key Laboratory of Sichuan Province, Chengdu, 610106, China.
Sci Rep. 2024 Dec 28;14(1):31055. doi: 10.1038/s41598-024-82255-4.
This study offers a comprehensive analysis of the Perturbed Schrödinger -Hirota Equation (PSHE), crucial for understanding soliton dynamics in modern optical communication systems. We extended the traditional Nonlinear Schrödinger Equation (NLSE) to include higher-order nonlinearities and spatiotemporal dispersion, capturing the complexities of light pulse propagation. Employing the modified auxiliary equation method and Adomian Decomposition Method (ADM), we derived a spectrum of exact traveling wave solutions, encompassing exponential, rational, trigonometric, and hyperbolic functions. These solutions provide insights into soliton behaviors across diverse parameters, essential for optimizing fiber optic systems. The precision of our analytical solutions was validated through numerical solutions, and we explored modulation instability, revealing conditions for soliton formation and evolution. The findings have significant implications for the design and optimization of next-generation optical communication technologies.
本研究对微扰薛定谔-广田方程（PSHE）进行了全面分析，这对于理解现代光通信系统中的孤子动力学至关重要。我们扩展了传统的非线性薛定谔方程（NLSE），以纳入高阶非线性和时空色散，从而捕捉光脉冲传播的复杂性。采用改进的辅助方程法和阿达姆分解法（ADM），我们推导了一系列精确的行波解，包括指数函数、有理函数、三角函数和双曲函数。这些解为不同参数下的孤子行为提供了见解，这对于优化光纤系统至关重要。我们通过数值解验证了解析解的精度，并研究了调制不稳定性，揭示了孤子形成和演化的条件。这些发现对下一代光通信技术的设计和优化具有重要意义。
