Estimates for the three-wave interaction of surface water waves
Estimates for the three-wave interaction of surface water waves
复制标题
表面水波三波相互作用的估计
DOI：
10.1017/s0956792503005163
复制
发表时间：
2003
影响因子：
1.9
通讯作者：
C. Wayne
中科院分区：
文献类型：
--
作者：
G. Schneider;C. Wayne
三波相互作用方程描述了三波的共振、二次、非线性相互作用。它们作为振幅方程在非线性光学、流体力学和等离子体物理的基本方程的渐近还原中获得。这些方程是完全可积的，并且在过去几年中一直是深入研究的主题。本文的目的是证明通过这个系统得到的近似和原始物理系统的解之间的精确估计。虽然三波相互作用模型被认为是描述了一些不同的物理模型，我们限制注意它的应用程序作为一个模型的共振相互作用的水波弱表面张力。
The equations for three-wave interaction describe the resonant, quadratic, nonlinear interaction of three waves. They are obtained as amplitude equations in an asymptotic reduction of the basic equations of nonlinear optics, fluid mechanics, and plasma physics. These equations are completely integrable and have been the subject of intensive research in the last years. It is the purpose of this paper to prove exact estimates between the approximations obtained via this system and solutions of the original physical system. Although the three-wave interaction model is believed to describe a number of different physical models we restrict attention to its application as a model of the resonant interaction of water waves subject to weak surface tension.