分数非线性施罗丁格方程:孤独流,调制不稳定性和极端的流波
Ming Zhong1,2, Weifang Weng3, Boling Guo4
1KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.
Chaos (Woodbury, N.Y.)
|January 13, 2025
概括
这项研究探讨了分数非线性系统中的流波. 一个特定的莱维指数范围增加了流波的概率由于更广泛的不稳定性,但也减缓了单子,抑制碰撞.
科学领域:
- 非线性物理学 非线性物理学
- 量子光学是一种量子光学.
- 流体动力学 流体动力学
背景情况:
- 一维的分数非线性施罗丁格方程 (FNLS) 模拟了非线性光学,斯-爱因斯坦凝结体和等离子体物理学中的现象.
- 孤独流和流波形成是非线性系统中的关键现象.
- 了解分数动力学对这些现象的影响至关重要.
研究的目的:
- 在一维的FNLS方程中系统地探索单独的乱现象和流波的出现.
- 调查莱维指数 (α) 对流波概率和单子动态的作用.
- 阐明驱动在分数非线性系统中的流波形成的潜在机制.
主要方法:
- 数字模拟以小噪声调节的平面波启动.
- 使用统计指数,分析非静止流的普遍模式.
- 检查波动光谱,第四阶时刻和概率密度函数.
主要成果:
- 莱维指数 (α) 的特定范围显著增加了流波发生的概率,这与扩大调制不稳定性有关.
- 通过光谱,瞬间和概率分布分析证实了更高的流波概率.
- 降低α降低了单子传播速度,通过碰撞抑制了高振幅的流波生成,创造了竞争机制.
结论:
- 莱维指数在分数非线性系统中的流波形成中发挥着关键的双重作用.
- 虽然扩大了调制不稳定性,但较低的α值阻碍了单子的移动性,影响了流波动力学.
- 这些发现为未来的研究提供了对分数非线性系统中流波机制的更深入的见解.
相关概念视频
01:07Interference and Superposition of Waves
4.8K
When two waves of the same nature occur in the same region simultaneously, they result in interference. Interference of waves implies that the net effect of the waves is the sum of the individual waves' effects. However, it does not imply that the individual waves affect the propagation of other waves.
Interference occurs in mechanical waves, such as sound waves, waves on a string, and surface water waves. Mechanical waves correspond to the physical displacement of particles. Hence,...
Interference occurs in mechanical waves, such as sound waves, waves on a string, and surface water waves. Mechanical waves correspond to the physical displacement of particles. Hence,...
4.8K
01:25Poisson's And Laplace's Equation
2.6K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
2.6K
01:27Traveling Waves: Lossless Lines
118
The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx and a shunt capacitance CΔx.
118
01:16Shock Waves
2.0K
While deriving the Doppler formula for the observed frequency of a sound wave, it is assumed that the speed of sound in the medium is greater than the source's speed through it. When this condition is breached, a shock wave occurs.
When the source's speed approaches the speed of sound, constructive interference between successive wavefronts emitted by the source occurs immediately behind it. Initially, scientists believed that this constructive interference would result in such high...
When the source's speed approaches the speed of sound, constructive interference between successive wavefronts emitted by the source occurs immediately behind it. Initially, scientists believed that this constructive interference would result in such high...
2.0K
01:03Modes of Standing Waves - I
2.9K
A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This...
2.9K
02:45The Quantum-Mechanical Model of an Atom
41.9K
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
41.9K