Analysis of the neighborhood of a smooth caustic for true-amplitude one-way wave equations

doi:10.1016/j.wavemoti.2006.01.003

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	Analysis of the neighborhood of a smooth caustic for true-amplitude one-way wave equations
	Bleistein, N ; Zhang, Y ; Zhang, GQ
	2006-04-01
发表期刊	WAVE MOTION
ISSN	0165-2125
卷号	43 期号:4 页码:323-338
摘要	In earlier papers it was shown that true-amplitude one-way wave equations provide "true amplitude" in the sense that the WKBJ or ray-theoretic solutions agree with the corresponding solutions of the full (two-way) wave equation. In the neighborhood of smooth caustics - smooth envelopes of rays - these ray-theoretic solutions break down with the predicted amplitudes of the solutions becoming infinite. For the two-way wave equation, that breakdown is well understood. The exact solution of the wave equation remains finite and it is only the WKBJ formalism that fails. Asymptotic solutions have been developed using higher functions (Airy functions). These solutions remain finite in a neighborhood of smooth caustics, adequately describing the exact solution, even in the limit where the observation point is on the caustic. A corresponding theory for the one-way wave equations is not yet available. However, numerical examples indicate that the solutions of the one-way wave equations remain finite and smooth near caustics. Furthermore, the mechanism for deriving the uniformly valid WKBJ solutions near smooth caustics strongly suggests that the uniform theory as derived for the two-way wave equation should be extendable to the one-way wave equation. Absent that extension, we present here a specific example in which we can analytically derive a uniformly valid asymptotic expansion near a smooth caustic via a standard extension of the method of stationary phase designed to deal with the neighborhood of smooth caustics. (C) 2006 Elsevier B.V. All rights reserved.
关键词	airy functions one-way wave equation ray theory smooth caustics stationary phase uniform asymptotic expansion
DOI	10.1016/j.wavemoti.2006.01.003
语种	英语
WOS研究方向	Acoustics ; Mechanics ; Physics
WOS类目	Acoustics ; Mechanics ; Physics, Multidisciplinary
WOS记录号	WOS:000237346800004
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/3186
专题	中国科学院数学与系统科学研究院
通讯作者	Bleistein, N
作者单位	1.Colorado Sch Mines, Dept Geophys, Ctr Wave Phenomena, Golden, CO 80401 USA 2.Veritas DGC Inc, Houston, TX 77072 USA 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Eng, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Bleistein, N,Zhang, Y,Zhang, GQ. Analysis of the neighborhood of a smooth caustic for true-amplitude one-way wave equations[J]. WAVE MOTION,2006,43(4):323-338.
APA	Bleistein, N,Zhang, Y,&Zhang, GQ.(2006).Analysis of the neighborhood of a smooth caustic for true-amplitude one-way wave equations.WAVE MOTION,43(4),323-338.
MLA	Bleistein, N,et al."Analysis of the neighborhood of a smooth caustic for true-amplitude one-way wave equations".WAVE MOTION 43.4(2006):323-338.