非线性水波Hamilton系统理论与应用研究进展

注意：本论文已在《力学进展》 28卷4期,521-531页, 1998年11月发表
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张宝善, 卢东强, 戴世强, 程友良
（上海大学，上海市应用数学和力学研究所，上海，200072）

摘要： 概述了辛几何理论与辛算法在Hamilton力学中的应用，综述非线性水波的Hamilton理论研究进展。阐述非线性水波Hamilton变分原理与方法的优越性与局限性，探讨KdV方程和BBM方程的Hamilton描述、对称性与守恒律。提出非线性水波Hamilton描述研究中有待进一步研究的问题和解法设想。
关键词： Hamilton变分原理，辛几何，非线性水波，Hamilton系统，对称性与守恒律

Research progress on theories and applications of Hamiltonian system in nonlinear water waves 

Zhang Baoshan, Lu Dongqiang, Dai Shiqiang, Cheng Youliang
(Shanghai Institute of Applied Mathematics & Mechanics, Shanghai University, Shanghai, China, 200072)

Abstract: This paper is a summary of the applications of symplectic theories algorithms to Hamiltonian mechanics and the research progress Hamiltonian formulation for nonlinear water waves. The advantages and limitations of Hamiltonian variational principle and approaches for nonlinear water waves are discussed. In addition, it includes also discussions on the Hamiltonian formalism, symmetry and conservation laws of KdV equation and BBM equation and comments on the problems concerned.
Keywords: Hamiltonian principle, symplectic geometry, nonlinear water waves, Hamiltonian systems, symmetry and conservation laws.

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

2、Free-surface waves and far wakes generated by a floating body in a viscous fluid

3、新型Poisson 括号意义下的无穷维Lie代数

4、INTERACTION OF VISCOUS WAKES WITH A FREE SURFACE

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