分数单子与局部缺陷的相互作用:稳定和分散
Thawatchai Mayteevarunyoo1, Boris A Malomed2,3
1Department of Electrical and Computer Engineering, Faculty of Engineering, Naresuan University, Phitsanulok 65000, Thailand.
Chaos (Woodbury, N.Y.)
|March 19, 2025
概括
非线性介质中的分数单子可以通过对缺陷进行固定来稳定. 这项研究表明,捕获潜力如何稳定这些单子,其结果是由瓦希托夫-科洛科洛夫标准预测的.
科学领域:
- 非线性光学是一种非线性光学.
- 分数微积分的微积分计算.
- 索利顿的动力学
背景情况:
- 在具有分数衍射的非线性介质中,soliton稳定性至关重要.
- 分数单子在均介质中往往不稳定,特别是在立方或五度自聚焦的介质中.
- 光学波导表现出有效的分数衍射,使得单子稳定成为一个关键的挑战.
研究的目的:
- 为了研究使用三角函数捕获潜力的分数单子的稳定.
- 分析莱维指数 (LI) α在单离子稳定中的作用.
- 用变量近似法 (VA) 和瓦希托夫-科洛科洛夫标准来比较数值发现.
主要方法:
- 用三角函数潜力的分数非线性施罗丁格方程的数值模拟.
- 使用变量近似法 (VA) 进行分析处理.
- 应用瓦希托夫-科洛科洛夫标准来预测不稳定的边界.
主要成果:
- 分数单子通过在立方 (α=1) 和五度 (α<2) 自聚焦介质中固定到三角函数缺陷来稳定.
- 根据莱维指数 (LI) α,观察到完全和部分稳定效应.
- 瓦希托夫-科洛科洛夫标准准确地预测了不稳定性边界.
- 不稳定的单体可以转化为振荡呼吸者.
- 变量近似为较低的LI值 (更强的分数) 提供了准确的结果.
- 有缺陷的碰撞显示出不同的结果:反弹,分裂和通道.
结论:
- 德尔塔功能的捕获潜能有效地稳定了固有的不稳定的分数单子.
- 稳定机制取决于自聚焦非线性类型和莱维指数 (LI) α.
- 变量近似是分析分数单子动态的一个可靠工具,特别是在更高的分数度.
- 该研究提供了对工程光学波导系统中单子行为的见解.
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