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INFINITE DIMENSIONAL LIE ALGEBRA WITH A NEW POISSON BRACKET 1)[J]. Chinese Journal of Theoretical and Applied Mechanics, 1998, 30(3): 307-313. DOI: 10.6052/0459-1879-1998-3-1995-131
Citation: INFINITE DIMENSIONAL LIE ALGEBRA WITH A NEW POISSON BRACKET 1)[J]. Chinese Journal of Theoretical and Applied Mechanics, 1998, 30(3): 307-313. DOI: 10.6052/0459-1879-1998-3-1995-131
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INFINITE DIMENSIONAL LIE ALGEBRA WITH A NEW POISSON BRACKET 1)

  • 上海大学上海市应用数学和力学研究所

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  • For the Hamiltonian formulation of the Korteweg de Vires equation (KdVequation), C.S. Gardner defined a Poisson bracket. In this paper a brand new bracket is defined. It is easily verified that the new bracket possesses three properties of the Poisson bracket, bilinearity,skew symmetry, Jacobi identity. The new Poisson bracket has a close connection with C.S. Gardner's definition. In the framework of the new Poisson bracket, all the first integrals of the KdV equation constitute an infinite dimension...
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