不完全整合的单元方程的异面理论
1Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow 108840, Russia.
Chaos (Woodbury, N.Y.)
|September 6, 2023
概括
我们用分散冲击波理论揭示了非线性波脉冲如何转化为单子列车. 一个保存的数量导致一个量化规则,预测单子的属性和匹配的数值结果.
科学领域:
- 非线性物理学 非线性物理学
- 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:
- 非线性波脉冲随着时间的推移而演变.
- 分散式冲击波 (DSW) 描述了波浪断裂和振荡形成.
- 孤独子是稳定的,局部化的非线性波.
研究的目的:
- 开发一种理论,用于将非线性波脉冲转化为单子列车.
- 为了在DSW中的振荡数量和出现的单子数量之间建立联系.
- 为了推导出一个量子化规则来预测单子特征.
主要方法:
- 使用分散式冲击波理论.
- 在无分散流中应用保存量概念.
- 使用波因卡雷-卡坦积分不变量.
- 与波尔-索默菲尔德式量子化规则相关的不变量.
主要成果:
- 冲击波中非线性振荡的数量直接对应于大时的单子数量.
- 一个保存在的量,与经典作用成比例,支配着这种转换.
- 波因卡雷-卡顿积分不变得出一个量子化规则,用于单一的固有值 (速度和特征).
- 分析预测与一般化失焦非线性施罗丁格方程的数值解决方案保持一致.
结论:
- 该研究为理解非线性波脉冲到单子列车转换提供了理论框架.
- 衍生量子化规则提供了一种方法来预测非对称单质子的属性.
- 这些发现通过数值模拟得到验证,证实了理论的准确性.
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