Ma Wen-xiu. A Hierarchy of Liouville Integrable Finite-Dimensional Hamiltonian Systems[J]. Applied Mathematics and Mechanics, 1992, 13(4): 349-357.
Citation: Ma Wen-xiu. A Hierarchy of Liouville Integrable Finite-Dimensional Hamiltonian Systems[J]. Applied Mathematics and Mechanics, 1992, 13(4): 349-357.

A Hierarchy of Liouville Integrable Finite-Dimensional Hamiltonian Systems

  • Received Date: 1990-01-31
  • Publish Date: 1992-04-15
  • 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.
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  • [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.
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