Solutions to the Hierarchy of the Periodic Toda Lattices

  • L. Trlifaj
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 488)


The hierarchy of the periodic Toda lattices is derived by means of the Appelle transformation. Members of the hierarchy are determined by equations of motion, by Hamiltonians and Lax pairs. Only two- and three-particle systems besides the basic Toda lattice are solved by quadratures in accordance with the Stäckel theorem. Other members of the hierarchy assume the solving of the polynomial equation, the degree of which is higher than four.


Poisson Bracket Toda Lattice Elementary Symmetric Function Toda System Abelian Differential 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • L. Trlifaj
    • 1
  1. 1.Institute of PhysicsPraha 8Czech Republic

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