{"title":"Kelvin’s method of stationary phase?","authors":"P.A. Martin","doi":"10.1016/j.wavemoti.2024.103481","DOIUrl":null,"url":null,"abstract":"<div><div>The method of stationary phase is a standard technique for estimating the value of an oscillatory integral when a certain parameter in the integrand becomes large. The basic method was sketched in 1887 by Sir William Thomson (before he became Lord Kelvin) in a short paper, and applied by him to problems in the theory of linear water waves. The contents, context and consequences of his paper are discussed. Inevitably, earlier authors (such as Stokes and Riemann) could stake claims on the method, but we leave it to the reader to decide, based on the evidence presented.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"134 ","pages":"Article 103481"},"PeriodicalIF":2.1000,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wave Motion","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165212524002117","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ACOUSTICS","Score":null,"Total":0}
引用次数: 0
Abstract
The method of stationary phase is a standard technique for estimating the value of an oscillatory integral when a certain parameter in the integrand becomes large. The basic method was sketched in 1887 by Sir William Thomson (before he became Lord Kelvin) in a short paper, and applied by him to problems in the theory of linear water waves. The contents, context and consequences of his paper are discussed. Inevitably, earlier authors (such as Stokes and Riemann) could stake claims on the method, but we leave it to the reader to decide, based on the evidence presented.
期刊介绍：
Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics.
The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
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