Transverse instability of solitary-wave states of the water-wave problem
Transverse instability of solitary-wave states of the water-wave problem
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DOI：
10.1017/s0022112001004530
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发表时间：
2001-07
影响因子：
3.7
通讯作者：
T. Bridges
中科院分区：
文献类型：
--
作者：
T. Bridges
孤立波的横向稳定性和不稳定性对应于一类沿基本孤立波方向的横向传播的扰动。本文从模型方程和全水波方程两方面考虑水波问题中孤立波的横向不稳定性问题。一个新的通用的横向不稳定性的几何条件形成的骨干分析。该理论首先说明了应用模型偏微分方程的水波，如KP方程，然后将其应用于完整的水波问题。这是第一个理论提出的孤立波的横向不稳定性的全水波问题。该理论建议引入一个新的功能的水波，其重要性是建议的数学结构。没有明确的计算，该理论是用来争论的孤立波的水波问题，分叉弗劳德数单位的基本类，很可能是稳定的横向扰动，即使在大幅度。
Transverse stability and instability of solitary waves correspond to a class of perturbations that are travelling in a direction transverse to the direction of the basic solitary wave. In this paper we consider the problem of transverse instability of solitary waves for the water-wave problem, from both the model equation point of view and the full water-wave equations. A new universal geometric condition for transverse instability forms the backbone of the analysis. The theory is first illustrated by application to model PDEs for water waves such as the KP equation, and then it is applied to the full water-wave problem. This is the first theory proposed for transverse instability of solitary waves of the full water-wave problem. The theory suggests the introduction of a new functional for water waves, whose importance is suggested by the mathematical structure. Without explicit calculation, the theory is used to argue that the basic class of solitary waves of the water-wave problem, which bifurcate at Froude number unity, are likely to be stable to transverse perturbations, even at large amplitude.