Geodesic
Nonuniqueness of solutions of the problem of solitary waves and bifurcation of critical points
Izvestiya. Mathematics , Tome 38 (1992) no. 2, pp. 333-357

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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. 
@article{IM2_1992_38_2_a5,
     author = {P. I. Plotnikov},
     title = {Nonuniqueness of solutions of the problem of solitary waves and bifurcation of critical points},
     journal = {Izvestiya. Mathematics },
     pages = {333--357},
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     volume = {38},
     number = {2},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1992_38_2_a5/}
}
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P. I. Plotnikov. Nonuniqueness of solutions of the problem of solitary waves and bifurcation of critical points. Izvestiya. Mathematics , Tome 38 (1992) no. 2, pp. 333-357. http://geodesic.mathdoc.fr/item/IM2_1992_38_2_a5/