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Theoretical and Mathematical Physics

, Volume 143, Issue 1, pp 515–528 | Cite as

Truncations of Toda chains and the reduction problem

  • I. T. Habibullin
Article

Abstract

We prove that the generalized Toda chains corresponding to simple Lie algebras of type D are reductions of chains corresponding to Lie algebras of type A.

Keywords

generalized Toda chains Darboux integrability Laplace invariants Lax pair simple Lie algebras 

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REFERENCES

  1. 1.
    A. B. Shabat and R. I. Yamilov, “Exponential systems of type I and Cartan matrices [in Russian],” Preprint, Bashkir Branch, Acad. Sci. USSR, Ufa (1981).Google Scholar
  2. 2.
    M. A. Olshanetsky and A. M. Perelomov, Phys. Rep., 71, 313–400 (1981).Google Scholar
  3. 3.
    A. N. Leznov and M. V. Saveliev, Group Methods of Integration of Nonlinear Dynamical Systems [in Russian], Nauka, Moscow (1985); English transl.: Group-Theoretical Methods for Integration of Nonlinear Dynamical Systems, Birkhäuser, Basel (1992).Google Scholar
  4. 4.
    S. P. Tsarev, Theor. Math. Phys., 122, 121–133 (2000).Google Scholar
  5. 5.
    G. Darboux, Lecons sur la théorie générale des surfaces et les applications gé ométriques du calcul infinitésimal, Vol. 2, Gautier-Villars, Paris (1915).Google Scholar
  6. 6.
    E. K. Sklyanin, Funct. Anal. Appl., 21, No.2, 164–166 (1987).Google Scholar
  7. 7.
    I. T. Habibullin, Phys. Lett. A, 178, 369–375 (1993).Google Scholar
  8. 8.
    I. M. Anderson and N. Kamran, Duke Math. J., 87, 265–319 (1997).Google Scholar
  9. 9.
    A. V. Zhiber and V. V. Sokolov, Russ. Math. Surveys, 56, 61–101 (2001).Google Scholar
  10. 10.
    I. T. Habibullin and E. V. Gudkova, Funct. Anal. Appl., 38, No.2, 138–148 (2004); E. V. Gudkova and I. T. Habibullin, Theor. Math. Phys., 140, 1086–1094 (2004).Google Scholar
  11. 11.
    E. Goursat, Am. J. Math., 18, 347–385 (1896).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • I. T. Habibullin
    • 1
  1. 1.Institute of Mathematics, Ufa Science CenterRASUfaRussia

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