摘要
本文概述完全可积的Hamilton系统的研究,它的经典力学背景,以及作为理论框架的辛流形,着重考察从无穷维可积系统导出有限维可积系统的约化方法。分析了一些已有的结果,包括从孤子方程极点展开解导出的多体问题的可积性,对反散射方法的新认识,以及作者最近研究出的特征值问题的非线性化方法,用以获得新的有限维完全可积系统。
An outline is given for the study of completely integrable Hamiltonian systems, withits background in classical mechanics and the symplectic manifold as its theoretical frame work. Specialemphasis is laid on the reduction technique to obtain finite-dimensional integrable systems from infi-nite-dimensional ones. Quite a few already known results are analysed, including the integrability ofthe many-body problem induced by the polar-expansion solutions of soliton equations, a new under-standing of the inverse scattering method, and the approach of nonlinearization of eigenvalue problemto acquire new finite-dimensional completely integrable systems, developed by the author recently.
出处
《石家庄铁道大学学报（自然科学版）》
1989年第4期1-9,共9页
Journal of Shijiazhuang Tiedao University(Natural Science Edition)
基金
国家自然科学基金
关键词
有限维完全可积系统
辛流形
约化技术
finite-dimensional completely integrable system
symplectic manifold
reduction technique
