A hierarchy of Liouville integrable finite-dimensional Hamiltonian systems

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.

Tu, G.Z., Infinitesimal canonical transformations of generalized Hamiltonian equations,J. Phys. A: Math. Gen.,15 (1982), 277–285.

Abraham, R., J.E. Marsden and T. Ratiu,Manifolds, Tensor Analysis, and Applications, Addison-Wesley Publishing Company, Inc., Massachusetts (1983).

Arnold, V.I.,Mathematical Methods of Classical Mechanics, Second (Corrected) Printing, Springer-Verlag, New York (1980).

Olver, P.J.,Applications of Lie Groups to Differential Equations, Springer-Verlag, New York (1986).

Moser, J., Various aspects of integrable Hamiltonian systems,Dynamical Systems (Progress in Mathematics,8), (Ed., J. Guckenheimer, et al., Birkhaäuser, Boston (1980), 233–289.

Moser, J., Three integrable Hamiltonian systems connected with isospectral deformations,Advances in Math.,16 (1975), 197–220.

Adler, M., Some finite dimensional integrable systems and their scattering behavior,Commun. Math. Phys.,55 (1975), 195–230.

Cao, C.W., Nonlinearization of the Lax system for AKNS hierarchy,Science in China, A, 7 (1989), 701–707, (in Chinese)

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.

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.

Tu, G.Z., On complete integrability of a large class of finite-dimensional Hamiltonian systems,Advances in Math. (China),20, 1 (1991), 60–74.

Ma, W.X., A new involutive system of polynomials and its classical integrable systems,Chinese Science Bulletin,35, 22 (1990), 1853–1858.

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.

Cao, C.W., Confocal involutive system and some kind of AKNS eigenvalue problems,Henan Science,5, 1 (1987), 1–10. (in Chinese)