Dispersive dynamics in the characteristic moving frame
Dispersive dynamics in the characteristic moving frame
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特征运动框架中的色散动力学
DOI：
10.1098/rspa.2018.0784
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Daniel J. Ratliff
中科院分区：
文献类型：
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作者：
Daniel J. Ratliff
提出了一种由无色散Whitham调制方程(WMES)自动产生色散的机制，它依赖于移动标架的使用。这一速度被选为Whitham系统线性化后出现的特征之一，并假设这些是真实的(因此WME是双曲线的)，将WME变形为升压坐标下的Korteweg-de Vries(KdV)方程。值得注意的是，KdV方程的系数是通用的，因为它们是由原始拉格朗日密度的抽象性质决定的。给出了该理论的两个说明性实例，以说明如何在实践中构建KDV。首先是对KdV方程从浅水流动的推导进行修正，以突出本文的理论如何适用于现有的文献。第二个是一个复杂的Klein-Gordon系统，提供了一种只有在使用移动标架的情况下才可能出现KdV方程的情况。
A mechanism for dispersion to automatically arise from the dispersionless Whitham Modulation equations (WMEs) is presented, relying on the use of a moving frame. The speed of this is chosen to be one of the characteristics which emerge from the linearization of the Whitham system, and assuming these are real (and thus the WMEs are hyperbolic) morphs the WMEs into the Korteweg-de Vries (KdV) equation in the boosted coordinate. Strikingly, the coefficients of the KdV equation are universal, in the sense that they are determined by abstract properties of the original Lagrangian density. Two illustrative examples of the theory are given to illustrate how the KdV may be constructed in practice. The first being a revisitation of the derivation of the KdV equation from shallow water flows, to highlight how the theory of this paper fits into the existing literature. The second is a complex Klein–Gordon system, providing a case where the KdV equation may only arise with the use of a moving frame.
对称性、相位调制和非线性波
DOI：
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发表时间：
2017
期刊：
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影响因子：
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作者：
Bridges
通讯作者：
Bridges