NONUNIQUENESS OF SOLUTIONS OF THE PROBLEM OF SOLITARY WAVES AND BIFURCATION OF CRITICAL POINTS OF SMOOTH FUNCTIONALS
NONUNIQUENESS OF SOLUTIONS OF THE PROBLEM OF SOLITARY WAVES AND BIFURCATION OF CRITICAL POINTS OF SMOOTH FUNCTIONALS
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孤波问题解的非唯一性及光滑泛函临界点分岔
DOI：
10.1070/im1992v038n02abeh002202
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
P. Plotnikov
中科院分区：
文献类型：
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作者：
P. Plotnikov
研究了理想流体表面上的孤波问题。利用变分原理证明，对于无限的弗劳德数的值集，这个问题至少有两个几何上不同的解。给出了赋范空间中光滑泛函单参数族退化临界点存在的充分条件。
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.