## 留言板

 引用本文: 卢东强, 戴世强, 张宝善. 一个二流体系统中非线性水波的Hamilton描述[J]. 应用数学和力学, 1999, 20(4): 331-336.
Lu Dongqiang, Dai Shiqiang, Zhang Baoshan. Hamiltonian Formulation of Nonlinear Water Waves in a Two-Fluid System[J]. Applied Mathematics and Mechanics, 1999, 20(4): 331-336.
 Citation: Lu Dongqiang, Dai Shiqiang, Zhang Baoshan. Hamiltonian Formulation of Nonlinear Water Waves in a Two-Fluid System[J]. Applied Mathematics and Mechanics, 1999, 20(4): 331-336.

## 一个二流体系统中非线性水波的Hamilton描述

###### 作者简介:卢东强(1972~ ),男,助教,硕士.
• 中图分类号: O353.2

## Hamiltonian Formulation of Nonlinear Water Waves in a Two-Fluid System

• 摘要: 讨论了一个二流体系统中非线性水波的Hamilton描述,该系统由水平固壁之上的两层常密度不可压无粘流体组成,上表面为自由面.文中将速度势函数展开成垂向坐标的幂级数,在浅水长波的假定下,取下层流体的“动厚度”与上层流体的“折合动厚度”为广义位移、界面上和自由面上的速度势为广义动量,根据Hamilton原理并运用Legendre变换导出该系统的Hamilton正则方程,从而将单层流体情形的结果推广到分层流体的情形.
•  [1] Luke L C.A variational principle for a fluid with a free surface[J].J Fluid Mech,1967,27:395~397. [2] Whitham G B.Variational methods and application to water waves[J].Proc Roy Soc A,1967,299(1):6~25. [3] Zakharov V E.Stability of periodic wave of finite amplitude on the surface of a deep fluid[J].J Appl Mech Tech Phys,1968,2(2):190~194. [4] Miles J W.On Hamilton's principle for surface waves[J].J Fluid Mech,1977,83:153~158. [5] Milder D M.A note regarding “On Hamilton's princilple for surfaces waves”[J].J Fluid Mech,1977,83:159~161. [6] Benjamin T B,Olver P J.Hamiltonian structure,symmetries and conservation laws for water wave[J].J Fluid Mech,1982,125:137~185. [7] 张宝善,卢东强,戴世强,等.非线性水波 Hamilton 系统理论与应用研究进展[J].力学进展,1998,28(4):521~531. [8] Craig W,Groves M D.Ham iltonian long-wave approximations to the water waves problems[J].Wave Motion,1994,19:367~389 [9] 卢东强,戴世强,张宝善.非线性水波无穷维 Hamilton 结构[A].见:程昌钧、戴世强、刘宇陆主编.现代数学和力学(MMM-Ⅶ)[C].上海:上海大学出版社,1997,387~390. [10] 戴世强.一个二流体系统中两对孤立波的相互作用[J].中国科学,A 辑,1983,26:1007~1017.

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##### 出版历程
• 收稿日期:  1997-12-24
• 修回日期:  1998-08-27
• 刊出日期:  1999-04-15

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