{"title":"二维Stokes非线性波的研究","authors":"N. Khatiashvili","doi":"10.37394/232020.2022.2.3","DOIUrl":null,"url":null,"abstract":"The Stokes nonlinear waves associated with the nonlinear problem of a free boundary with peaks in incompressible heavy fluid are studied in 2D. In the early works of the author by using the conformal mapping method this problem was reduced to the nonlinear integral equation with the weakly singular kernel. In this paper one parameter of the mapping is chosen sufficiently small and the equation is linearized. The approximate solution of the linearized equation is obtained. The profile of the free boundary is plotted by means of Maple-12.","PeriodicalId":93382,"journal":{"name":"The international journal of evidence & proof","volume":"9 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On the Stokes Nonlinear Waves in 2D\",\"authors\":\"N. Khatiashvili\",\"doi\":\"10.37394/232020.2022.2.3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Stokes nonlinear waves associated with the nonlinear problem of a free boundary with peaks in incompressible heavy fluid are studied in 2D. In the early works of the author by using the conformal mapping method this problem was reduced to the nonlinear integral equation with the weakly singular kernel. In this paper one parameter of the mapping is chosen sufficiently small and the equation is linearized. The approximate solution of the linearized equation is obtained. The profile of the free boundary is plotted by means of Maple-12.\",\"PeriodicalId\":93382,\"journal\":{\"name\":\"The international journal of evidence & proof\",\"volume\":\"9 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-03-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The international journal of evidence & proof\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37394/232020.2022.2.3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The international journal of evidence & proof","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37394/232020.2022.2.3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Stokes nonlinear waves associated with the nonlinear problem of a free boundary with peaks in incompressible heavy fluid are studied in 2D. In the early works of the author by using the conformal mapping method this problem was reduced to the nonlinear integral equation with the weakly singular kernel. In this paper one parameter of the mapping is chosen sufficiently small and the equation is linearized. The approximate solution of the linearized equation is obtained. The profile of the free boundary is plotted by means of Maple-12.
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