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)

Abstract

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.

Keywords

Peri 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ashok D., and Susumo O. (1989), Ann. Phys.(N.Y.) 158, 215.Google Scholar
  2. Appelle M. (1882), Comptes Rendus Acad. Sci. Paris 91, 212.Google Scholar
  3. Levi-Civita T., and Amaldi U. (1927): Lezioni di Mecanica Razionale, Vol.II, Bologna 1927.Google Scholar
  4. Pars L.A. (1964): A Treatise on Analytical Dynamics, Heinemann, London 1964.Google Scholar
  5. Toda M. (1981): Theory of Nonlinear Lattices, Springer Vlg., Berlin, 1981.CrossRefMATHGoogle Scholar
  6. Kadoma Y., and Ye J. (1996), Physics D 91, 324.Google Scholar
  7. Date E., and Tanaka S. (1976), Prog. Theor. Phys. Suppl. 59, 107.ADSCrossRefMathSciNetGoogle Scholar
  8. Dubrovin B.A. (1981), Uspekhi Mat. Nauk 36, 11.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

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

Personalised recommendations