{"title":"孤立波问题解的非唯一性与光滑泛函的临界点分岔","authors":"P. Plotnikov","doi":"10.1070/IM1992V038N02ABEH002202","DOIUrl":null,"url":null,"abstract":"The problem of solitary waves on the surface of an ideal fluid is considered. By means of a variational principle it is shown that for an infinite set of values of the Froude number this problem has at least two geometrically distinct solutions. Sufficient conditions are formulated for the existence of bifurcations of degenerate critical points of one-parameter families of smooth functionals defined in a normed space.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"44","resultStr":"{\"title\":\"NONUNIQUENESS OF SOLUTIONS OF THE PROBLEM OF SOLITARY WAVES AND BIFURCATION OF CRITICAL POINTS OF SMOOTH FUNCTIONALS\",\"authors\":\"P. Plotnikov\",\"doi\":\"10.1070/IM1992V038N02ABEH002202\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The problem of solitary waves on the surface of an ideal fluid is considered. By means of a variational principle it is shown that for an infinite set of values of the Froude number this problem has at least two geometrically distinct solutions. Sufficient conditions are formulated for the existence of bifurcations of degenerate critical points of one-parameter families of smooth functionals defined in a normed space.\",\"PeriodicalId\":159459,\"journal\":{\"name\":\"Mathematics of The Ussr-izvestiya\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-04-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"44\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-izvestiya\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/IM1992V038N02ABEH002202\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-izvestiya","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/IM1992V038N02ABEH002202","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
NONUNIQUENESS OF SOLUTIONS OF THE PROBLEM OF SOLITARY WAVES AND BIFURCATION OF CRITICAL POINTS OF SMOOTH FUNCTIONALS
The problem of solitary waves on the surface of an ideal fluid is considered. By means of a variational principle it is shown that for an infinite set of values of the Froude number this problem has at least two geometrically distinct solutions. Sufficient conditions are formulated for the existence of bifurcations of degenerate critical points of one-parameter families of smooth functionals defined in a normed space.
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