非线性水波Hamilton系统理论与应用研究进展  

RESEARcH PROGRESS ON THEORIES AND APPLICATIONS OF HAMILTONIAN SYSTEM IN NONLINEAR WATER WAVES

作　　者：张宝善[1] 卢东强[1] 戴世强[1] 程友良[1] 

机构地区：[1]上海大学

出　　处：《力学进展》1998年第4期521-531,共11页Advances in Mechanics

基　　金：国家自然科学基金

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．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.

关 键 词：变分原理 辛几何 非线性 水波 H系统 

分 类 号：O353.2[理学—流体力学]