Dispersive shock waves and modulation theory
Dispersive shock waves and modulation theory
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DOI：
10.1016/j.physd.2016.04.006
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发表时间：
2016-10-15
影响因子：
4
通讯作者：
Hoefer, M. A.
中科院分区：
文献类型：
--
作者：
El, G. A.;Hoefer, M. A.
人们对无耗散/弥散介质的流体动力学有越来越多的物理和数学兴趣。自从五十年前G.B.Whitham的开创性出版开启了弥散流体动力学的数学研究以来，这一领域已经有了大量的工作。然而，目前还没有关于弥散流体力学领域的全面调查。利用Whitham的平均理论作为主要的数学工具，我们回顾了过去50年来丰富的数学发展，重点是物理应用。色散流体动力学系统中基本的、大尺度的相干激励是一种扩展的、振荡的色散激波。在单向(Korteweg-de Vries方程)和双向(非线性薛定谔方程)色散流体力学的普适、可积和基本模型的背景下，详细分析了DSWs的宏观和微观性质。描述了一种不依赖于可积结构但揭示了重要的宏观DSW性质的DSW拟合过程。DSW理论随后被应用于许多物理应用：超流体、非线性光学、地球物理和流体动力学。最后，我们综述了一些最新的发展，包括非经典的离散波，离散波的相互作用，扰动和非均匀环境中的离散波，以及二维倾斜的离散波。(C)2016爱思唯尔B.V.保留所有权利。
There is growing physical and mathematical interest in the hydrodynamics of dissipationless/dispersive media. Since G.B. Whitham's seminal publication fifty years ago that ushered in the mathematical study of dispersive hydrodynamics, there has been a significant body of work in this area. However, there has been no comprehensive survey of the field of dispersive hydrodynamics. Utilizing Whitham's averaging theory as the primary mathematical tool, we review the rich mathematical developments over the past fifty years with an emphasis on physical applications. The fundamental, large scale, coherent excitation in dispersive hydrodynamic systems is an expanding, oscillatory dispersive shock wave or DSW. Both the macroscopic and microscopic properties of DSWs are analyzed in detail within the context of the universal, integrable, and foundational models for uni-directional (Korteweg-de Vries equation) and bidirectional (Nonlinear Schrodinger equation) dispersive hydrodynamics. A DSW fitting procedure that does not rely upon integrable structure yet reveals important macroscopic DSW properties is described. DSW theory is then applied to a number of physical applications: superfluids, nonlinear optics, geophysics, and fluid dynamics. Finally, we survey some of the more recent developments including non-classical DSWs, DSW interactions, DSWs in perturbed and inhomogeneous environments, and two-dimensional, oblique DSWs. (C) 2016 Elsevier B.V. All rights reserved.