模块化不稳定性,生成和 rogue 波的演变在一般化的分数非线性施罗丁格方程中与权力定律非线性和理性潜能
Zijian Zhou1, Zhenya Yan2,3
1School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, MOE, Beijing Normal University, Beijing 100875, China.
Chaos (Woodbury, N.Y.)
|October 7, 2024
概括
本研究探讨了分数非线性施罗丁格方程中的调制不稳定性 (MI) 和流波 (RWs). 理性潜能使可控制的RW和W形单子成为可能,进步非线性波现象的理解.
科学领域:
- 非线性光学是非线性光学.
- 数学物理学的数学物理.
- 波浪现象是一种波浪现象.
背景情况:
- 分数非线性施罗丁格方程 (FNLS) 描述了复杂的波动力学.
- 调制不稳定性 (MI) 和流波 (RW) 是非线性系统中的关键现象.
- 理性潜能提供了一种控制波浪行为的方法.
研究的目的:
- 研究具有理性潜力的概括式分数非线性施罗丁格方程 (FNLS) 中的调制不稳定性 (MI) 和流波 (RWs).
- 分析系统参数 (σ,α,g) 对连续波 (CW) 分散和不稳定性的影响.
- 探索可控制的流波 (RW) 和W形单子的生成,使用时间依赖和时间独立的理性潜能.
主要方法:
- 对于连续波 (CWs) 的分散关系的导出.
- 对调制不稳定性 (MI) 和流波 (RW) 生产的理论分析.
- 数字模拟以证实理论发现.
- 研究更高层次的RW和多RW解决方案.
主要成果:
- 调制不稳定性 (MI) 在聚焦模式中得到确认.
- 可控制的恶作剧波 (RWs) 在失焦模式中使用时间依赖的理性潜力激发.
- 稳定的W形单子产生与时间独立的理性潜能.
- 确定了更高阶RW发电的条件.
- 在失焦立方FNLS方程中观察到的分离,可控制的多个RW.
结论:
- 理性潜能有效地控制FNLS方程中的流波 (RW) 和单子动态.
- 该研究提供了一个更深入的了解MI和RWs在分数非线性系统.
- 这些发现为未来研究非线性波现象和潜在应用提供了途径.
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