Hamiltonian Structures of Soliton Equations via Constrained Variational Calculus

  • Tu Gui-zhang
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 30)

Abstract

We prove the following trace identity
$$\left( {\delta /\delta {u_\alpha }} \right)Tr\left( {K\partial U/\partial n} \right) = \left( {\partial {\mkern 1mu} /{\mkern 1mu} \partial n} \right)Tr\left( {K\partial U/{\mkern 1mu} \partial {u_\alpha }} \right),$$
(1)
where K satisfies the equation Kx=[U,K] and U=U(uα,n). We show that a number of known formulae, obtained previously by complicated calculation, are the special cases of this remarkable identity.

Keywords

Soliton 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Tu Gui-zhang
    • 1
  1. 1.Computing Center of Chinese Academy of SciencesBeijingPR China

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