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Mathematics of the USSR-Izvestiya, 1992, Volume 38, Issue 2, Pages 333–357
DOI: https://doi.org/10.1070/IM1992v038n02ABEH002202 (Mi im1013) 		 
This article is cited in 24 scientific papers (total in 24 papers)

Nonuniqueness of solutions of the problem of solitary waves and bifurcation of critical points of smooth functionals

P. I. Plotnikov
English version PDF (1476 kB) Citations (24) Russian version article
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DOI: https://doi.org/10.1070/IM1992v038n02ABEH002202
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.
Received: 13.11.1989
Bibliographic databases:
UDC: 517.9+532.5
MSC: 76B25, 35Q51
Language: English
Original paper language: Russian
Citation: P. I. Plotnikov, “Nonuniqueness of solutions of the problem of solitary waves and bifurcation of critical points of smooth functionals”, Math. USSR-Izv., 38:2 (1992), 333–357
Citation in format AMSBIB
\Bibitem{Plo91}
\by P.~I.~Plotnikov
\paper Nonuniqueness of solutions of the problem of solitary waves and bifurcation of critical points
of smooth functionals
\jour Math. USSR-Izv.
\yr 1992
\vol 38
\issue 2
\pages 333--357
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\zmath{https://zbmath.org/?q=an:0795.76017}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1992IzMat..38..333P}
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  • https://www.mathnet.ru/eng/im/v55/i2/p339
    • This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
     
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