一族Liouville可积的有限维Hamilton系统

马文秀

一族Liouville可积的有限维Hamilton系统

马文秀

复旦大学数学研究所上海

计量
- 文章访问数: 2095
- HTML全文浏览量: 127
- PDF下载量: 608
- 被引次数: 0
出版历程
- 收稿日期: 1990-01-31
- 刊出日期: 1992-04-15

A Hierarchy of Liouville Integrable Finite-Dimensional Hamiltonian Systems

Ma Wen-xiu

Institute of Mathematics, Fudan University, Shanghai

摘要

摘要: 本文生成了一族Liouville可积的Hamilton相流彼此可交换的有限维Hamilton系统,并且给出了一串对合的显式公共运动积分及其一组对合的显式生成元.
- 对合系 /
- 运动积分 /
- 生成子 /
- Hamilton系统 /
- 可积性
Abstract: A hierarchy of Liouville integrable finite-dimensional Hamiltonian systems whose Hamiltonian phase flows commute with each other is generated and an infinite number of involutive explicit common integrals of motion and a set of its involutive explicit generators are given.
- involutive system /
- integral of motion /
- generator /
- Hamiltonian system /
- integrability

HTML全文

参考文献(15)

[1]	Lax,P.D.,A Hamiltonian approach to the KdV and other equations,Nonlinear Evolution Equations,Ed.,M.G.Crandall,Academic Press,New York(1978),207-224.
[2]	Tu,G.Z.,Infinitesimal canonical transformations of generalized Hamiltonian equations,J.Phys.A: Math.Gen.,15(1982),277-285.
[3]	Abraham,R.,J.E.Marsden and T.Ratiu,Manifolds,Tensor Analysis,and Applications,Addison-Wesley Publishing Company,Inc.,Massachusetts(1983).
[4]	Arnold,V.I.,Mathematical Methods of Classical Mechanics,Second(Corrected) Printing,Springer-Verlag,New York(1980).
[5]	Olver,P.J.,Applications of Lie Groups to Differential Equations,Springer-Verlag,New York(1986).
[6]	Moser,J.,Various aspects of integrable Hamiitonian systems,Dynamical Systems(Progress in Mathematics,8),(Ed.,J.Guckenheimer,et al.,Birkhaüser,Boston(1980),233-289.
[7]	Moser,J.,Three integrable Hamiltonian systems connected with isospectral deformations,Advances in Math.,16(1975),197-220.
[8]	Adler,M.,Some finite dimensional integrable systems and their scattering behavior,Commun.Math.Phys.,55(1977),195-230.
[9]	Cao,C.W.,Nonlinearization of the Lax system for AKNS hierarchy,Science in China,A,7(1989),701-707.(in Chinese).
[10]	Zeng,Y.B.and Y.S.Li,Three kinds of constraints of potentials for KdV hierarchy,Acta Math.Sinica,New Series,6,3(1990),257-272.
[11]	Cao,C.W.and X,G.Geng,Classical integrable systems generated through nonlinearization of eigenvalue problems,Nonlinear Physics(Research Reports in Physics),Springer-Verlag,Berlin(1986),68-78.
[12]	Tu,G.Z.,On complete integrability of a large class of finite-dimensional Hamiltonian systems,Advances in Math.(China),20,1(1991),60-74.
[13]	马文秀,一个新的多项式对合系及其经典可积系统,科学通报,34(23)(1989),1770-1774.
[14]	Ma,W.X.,The confocal involutive system and the integrability of the nonlinearized Lax systems of AKNS hierarchy,Nonlinear Physics(Research Reports in Physics),Springer-Verlag,Berlin(1990),79-84.
[15]	曹策问,共焦对合系与一类AKNS特征值问题,河南科学,5(1)(1987),1-10.