{"title":"Exact Solution for Capillary Waves on the Surface of a Liquid of Finite Depth","authors":"M. M. Alimov","doi":"10.3103/s1066369x23090050","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>An attempt was made to reproduce, using the Schwartz function method, the well-known exact solution of Kinnersley to the problem of capillary waves on the surface of a liquid of finite depth. However, as a result, a new exact solution was obtained, which does not coincide with the solution of Kinnersley, although it is expressed in the same terms of Jacobi elliptic functions. The results of an independent numerical verification of the new solution are presented, confirming its reliability. The parametric analysis of the solution revealed, in particular, a nonmonotonic dependence of the wavelength and its amplitude on the Weber number.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"13 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1066369x23090050","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
An attempt was made to reproduce, using the Schwartz function method, the well-known exact solution of Kinnersley to the problem of capillary waves on the surface of a liquid of finite depth. However, as a result, a new exact solution was obtained, which does not coincide with the solution of Kinnersley, although it is expressed in the same terms of Jacobi elliptic functions. The results of an independent numerical verification of the new solution are presented, confirming its reliability. The parametric analysis of the solution revealed, in particular, a nonmonotonic dependence of the wavelength and its amplitude on the Weber number.
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