论文标题
真正的非线性及其与相位动力学中修改的Korteweg -de Vries方程的联系
Genuine Nonlinearity and its Connection to the Modified Korteweg - de Vries Equation in Phase Dynamics
论文作者
论文摘要
双曲波的研究涉及各种概念，这些概念有助于表征这些结构的发展方式。一个重要的方面是\ emph {真正的非线性}的概念，即冲击和稀有形成而不是接触不连续性的能力。在WHITHAM调制方程的上下文中，本文表明，真正的非线性丧失会导致以修改后的Korteweg De-Vries方程的形式出现一组分散性动力学，而不是波浪的演变。它的形式是普遍的，因为它的系数可以完全使用诸如保护定律和线性分散关系之类的基础波的线性特性编写。该洞察力应用于两个物理感兴趣的系统，一个是光学模型，另一个是一个分层的流体动力学实验，以证明如何使用它来提供有关这些系统中的波浪在丢失真正的非线性时如何发展的洞察力。
The study of hyperbolic waves involves various notions which help characterise how these structures evolve. One important facet is the notion of \emph{genuine nonlinearity}, namely the ability for shocks and rarefactions to form instead of contact discontinuities. In the context of the Whitham Modulation equations, this paper demonstrate that a loss of genuine nonlinearity leads to the appearance of a dispersive set of dynamics in the form of the modified Korteweg de-Vries equation governing the evolution of the waves instead. Its form is universal in the sense that its coefficients can be written entirely using linear properties of the underlying waves such as the conservation laws and linear dispersion relation. This insight is applied to two systems of physical interest, one an optical model and the other a stratified hydrodynamics experiment, to demonstrate how it can be used to provide insight into how waves in these systems evolve when genuine nonlinearity is lost.
