Fully localised solitary-wave solutions of the three-dimensional gravity-capillary water-wave problem

被引：55
作者：
Groves, M. D. [1 ]
Sun, S. -M.
机构：
[1] Univ Loughborough, Dept Math Sci, Loughborough LE11 3TU, Leics, England
来源：
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2008年 / 188卷 / 01期
基金：
美国国家科学基金会;
关键词：
D O I：
10.1007/s00205-007-0085-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A model equation derived by KADOMTSEV & PETVIASHVILI (Sov Phys Dokl 15:539-541, 1970) suggests that the hydrodynamic problem for three-dimensional water waves with strong surface-tension effects admits a fully localised solitary wave which decays to the undisturbed state of the water in every horizontal spatial direction. This prediction is rigorously confirmed for the full water-wave problem in the present paper. The theory is variational in nature. A simple but mathematically unfavourable variational principle for fully localised solitary waves is reduced to a locally equivalent variational principle with significantly better mathematical properties. The reduced functional is related to the functional associated with the Kadomtsev-Petviashvili equation, and a nontrivial critical point is detected using the direct methods of the calculus of variations.
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页码：1 / 91
页数：91
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