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首页> 外文期刊>SIAM Journal on Mathematical Analysis >SPATIAL DYNAMICS METHODS FOR SOLITARY GRAVITY-CAPILLARY WATER WAVES WITH AN ARBITRARY DISTRIBUTION OF VORTICITY
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SPATIAL DYNAMICS METHODS FOR SOLITARY GRAVITY-CAPILLARY WATER WAVES WITH AN ARBITRARY DISTRIBUTION OF VORTICITY

机译：旋涡任意分布的重力-毛细水波的空间动力学方法

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摘要

This paper presents existence theories for several families of small-amplitude solitarywave solutions to the classical two-dimensional water-wave problem in the presence of surface tension and with an arbitrary distribution of vorticity. Moreover, the established local bifurcation diagram for irrotational solitary waves is shown to remain qualitatively unchanged for any choice of vorticity distribution. The hydrodynamic problem is formulated as an infinite-dimensional Hamiltonian system in which the horizontal spatial direction is the timelike variable. A center-manifold reduction technique is employed to reduce the system to a locally equivalent Hamiltonian system with a finite number of degrees of freedom. Homoclinic solutions to the reduced system, which correspond to solitary water waves, are detected by a variety of dynamical systems methods.
机译：本文提出了在存在表面张力和任意涡度分布的情况下，经典二维水波问题的几个小振幅孤波解的存在性理论。此外，对于任何涡度分布的选择，已建立的非旋转孤波的局部分叉图显示在质上保持不变。流体动力学问题被表述为一个无限维的哈密顿系统，其中水平空间方向是时变变量。采用中心流形减少技术将系统简化为具有有限个自由度的局部等效哈密顿系统。通过各种动力学系统方法可以检测到简化系统的同宿解决方案，该解决方案对应于孤立水波。

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