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| 非线性水波Hamilton系统理论与应用研究进展 | |
| 引用本文： | 张宝善 卢东强. 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 |
| 作者姓名： | 张宝善 卢东强 |
| 作者单位： | [1]上海大学 [2]上海市应用数学和力学研究所 |
| 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 Ha |
RESEARcH PROGRESS ON THEORIES AND APPLICATIONS OF HAMILTONIAN SYSTEM IN NONLINEAR WATER WAVES |
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| Zhang Baoshan,Lu Dongqiang,Dai Shiqiang,Cheng Youliang. RESEARcH PROGRESS ON THEORIES AND APPLICATIONS OF HAMILTONIAN SYSTEM IN NONLINEAR WATER WAVES[J]. Advances in Mechanics, 1998, 28(4): 521-531 | |
| Authors: | Zhang Baoshan Lu Dongqiang Dai Shiqiang Cheng Youliang |
| Abstract: | This paper is a summary of the applications of symplectic theories and symplectic algorithms to Hamiltonian mechanics and the research progress Hamiltonian formulation for nonlinear water waves.The advanages and limitations of Hamiltonian variational principle and approaches for nonlineax water waves are discussed.In addition, it includes also discussions on the Hamiltonian formalism, symmetry and conseryation laws of KdV equation and BBM equation and comments on the problems concerned. |
| Keywords: | Hazniltonian principle symplectic geometry nonlinear water waves Hamiltonian systems symmetry and Conservation laws |
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