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Lie algebra contractions and symmetries of the Toda hierarchy

Journal of Physics A: Mathematical and General, ISSN: 0305-4470, Vol: 33, Issue: 28, Page: 5025-5040
2000
  • 38
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  • Citations
    38
    • Citation Indexes
      38
  • Captures
    4

Article Description

The Lie algebra L(△) of generalized and point symmetries of the equations in the Toda hierarchy is shown to be a semidirect sum of two infinite-dimensional Lie algebras, one perfect, the other Abelian. In the continuous limit the structure of the Lie algebra changes: a contraction occurs with the lattice spacing as the contraction parameter. In particular, for the Toda equation itself, a set of five elements, involving both point symmetries and generalized ones, contracts to the point symmetry algebra of the potential KdV equation.

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