Applied Mathematics and Mechanics

, Volume 24, Issue 1, pp 22–27 | Cite as

The Hamiltonian equations in some mathematics and physics problems

  • Chen Yong
  • Zheng Yu
  • Zhang Hong-qing


Some new Hamiltonian canonical system are discussed for a series of partial differential equations in Mathematics and Physics. It includes the Hamiltonian formalism for the symmetry second-order equation with the variable coefficients, the new nonhomogeneous Hamiltonian representation for fourth-order symmetry equation with constant coefficients, the one of MKdV equation and KP equation.

Key words

infinite dimensional Hamiltonian system Hamiltonian canonical system Hamiltonian operator MKdV (Modified Korteweg-de Vries) equation KP (Kadomtsev-Petviashvili) equation 

Chinese Library Classification


2000 MR Subject Classification

58E30 35Q72 49N45 74H30 


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  1. [1]
    FENG Kang. On difference schemes and symplectic geometry[A]. In: D Schmidt Ed.Proceeding of 1984 Beijing International Symposium on Differential Geometry and Differential Equations[C]. Beijing: Science Press, 1985, 42–58.Google Scholar
  2. [2]
    Olver P J.Applications of Lie Group to Differential Equations[M]. New York: Springer-Verlag, 1986.Google Scholar
  3. [3]
    Gardner C S. Korteweg-de Vries equations and generalization IV: The Korteweg-de Vries equations as a Hamiltonian system[J].J Math Phys, 1971,12(8):1548–1551.MATHCrossRefGoogle Scholar
  4. [4]
    Magri F. A simple model of the integrable Hamiltonian equation[J].J Math Phys, 1978,19(5): 1156–1162.MATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    Abraham R, Marsden J E, Ratiu T.Manifolds Tensor Analysis and Applications[M]. New York: Springer-Verlag, 1990.Google Scholar
  6. [6]
    ZHENG Yu, ZHANG Hong-qing. The canonical Hamilton representations in solid mechanics[J].Acta Mechanica Sinica, 1996,28(1):119–125. (in Chinese)MathSciNetGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2003

Authors and Affiliations

  • Chen Yong
    • 1
  • Zheng Yu
    • 2
  • Zhang Hong-qing
    • 1
  1. 1.Department of MathematicsDalian University of TechnologyDalianChina
  2. 2.Department of MathematicsEast China Normal UniversityShanghaiChina

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