Waves that Appear From Nowhere: Complex Rogue Wave Structures and Their Elementary Particles
Waves that Appear From Nowhere: Complex Rogue Wave Structures and Their Elementary Particles
复制标题
DOI：
10.3389/fphy.2020.612318
复制
发表时间：
2021-01
期刊：
影响因子：
--
通讯作者：
N. Akhmediev
中科院分区：
文献类型：
--
作者：
N. Akhmediev
非线性薛定谔方程在物理学中有广泛的应用，空间尺度从微米到千米不等。因此，它的解也是普适的，可以应用于水波、光学、等离子体和玻色-爱因斯坦凝聚。目前最著名的解是游隼解，它描述了不知从何处出现的波。这个解决方案描述了在时间和空间上都本地化的独特事件。按照水手们的说法，它们被称为“流氓浪”。正如彻底的数学分析所显示的那样，这些波具有不同于以前已知的任何其他非线性波的性质。游子波可以在更复杂的结构中充当“基本粒子”，也是非线性薛定谔方程的精确解。这些结构导致具有不同对称度的特定图案。其中一些类似于“原子状结构”。这些结构中的粒子数量不是任意的，而是满足严格的规则。在其他数学物理方程描述的系统中也可以观察到类似的结构：Hirota方程，Davey-Stewartson方程，Sasa-Satsuma方程，广义Landau-Lifshitz方程，复KdV方程，甚至描述核子与中性标量介子相互作用的耦合Higgs场方程。这意味着，流氓波的概念几乎进入了物理学的所有领域，包括基本粒子领域。
The nonlinear Schrödinger equation has wide range of applications in physics with spatial scales that vary from microns to kilometres. Consequently, its solutions are also universal and can be applied to water waves, optics, plasma and Bose-Einstein condensate. The most remarkable solution presently known as the Peregrine solution describes waves that appear from nowhere. This solution describes unique events localized both in time and in space. Following the language of mariners they are called “rogue waves”. As thorough mathematical analysis shows, these waves have properties that differ them from any other nonlinear waves known before. Peregrine waves can serve as ‘elementary particles’ in more complex structures that are also exact solutions of the nonlinear Schrödinger equation. These structures lead to specific patterns with various degrees of symmetry. Some of them resemble “atomic like structures”. The number of particles in these structures is not arbitrary but satisfies strict rules. Similar structures may be observed in systems described by other equations of mathematical physics: Hirota equation, Davey-Stewartson equations, Sasa-Satsuma equation, generalized Landau-Lifshitz equation, complex KdV equation and even the coupled Higgs field equations describing nucleons interacting with neutral scalar mesons. This means that the ideas of rogue waves enter nearly all areas of physics including the field of elementary particles.