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Theoretical and Mathematical Physics

, Volume 45, Issue 1, pp 843–854 | Cite as

The Toda chain as a reduced system

  • M. A. Ol'shanetskii
  • A. M. Perelomov
Article

Keywords

Toda Chain 
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Literature Cited

  1. 1.
    J. M. Sourian, Structure des Systems Dynamiques, Dynod, Paris (1970).Google Scholar
  2. 2.
    V. I. Arnol'd, Mathematical Methods in Classical Mechanics [in Russian], Nauka (1974).Google Scholar
  3. 3.
    J. Marsden and A. Weinstein, Rep. Math. Phys.,5, 121 (1974).Google Scholar
  4. 4.
    J. Moser, Preprint, Courant Institute of Mathematical Science, New York University (1978).Google Scholar
  5. 5.
    D. Kazhdan, B. Kostant, and S. Sternberg, Commun. Pure Appl. Math.,31, 481 (1978).Google Scholar
  6. 6.
    M. A. Ol'shanetskii and A. M. Perelomov, Funktsional. Analiz i Ego Prilozhen.,10, 86 (1976).Google Scholar
  7. 7.
    M. A. Ol'shanetskii and A. M. Perelomov, Funktsional. Analiz i Ego Prilozhen.,11, 75 (1977).Google Scholar
  8. 8.
    M. A. Olshanetsky and V.-B. K. Rogov, Ann. Inst. H. Poincaré,29, 169 (1978).Google Scholar
  9. 9.
    M. Toda, J. Phys. Soc. Jpn.,22, 431 (1967);23, 501 (1968).Google Scholar
  10. 10.
    M. Toda, Prog. Theor. Phys. Suppl.,45, 174 (1970).Google Scholar
  11. 11.
    M. Henon, Phys. Rev. B,9, 1924 (1974).Google Scholar
  12. 12.
    S. V. Manakov, Zh. Eksp. Teor. Fiz.,67, 543 (1974).Google Scholar
  13. 13.
    H. Flaschka, Phys. Rev. B,9, 1924 (1974).Google Scholar
  14. 14.
    H. Flaschka, Prog. Theor. Phys.,51, 703 (1974).Google Scholar
  15. 15.
    J. Moser, Lect. Notes Phys.,38, 97 (1975).Google Scholar
  16. 16.
    B. A. Dubrovin, V. B. Matveev, and S. P. Novikov, Usp. Mat. Nauk,31, 56 (1976).Google Scholar
  17. 17.
    T. Kotera and S. Yamazaki, Toda Lattice and Kac-Moerbeke's Equation; the General Solutions for the Scattering Problems, Preprint, Inst. of Phys. Univ. of Tsukuba, Niihari-gan, Ibaraki (1976).Google Scholar
  18. 18.
    M. Adler, Invent. Math.,50, 219 (1979).Google Scholar
  19. 19.
    A. G. Reiman, M. A. Semenov-Tyan-Shanskii, and I. E. Frenkel', Dokl. Akad. Nauk SSSR,244, 55 (1979).Google Scholar
  20. 20.
    I. M. Krichever, Usp. Mat. Nauk,33, 215 (1978).Google Scholar
  21. 21.
    M. A. Olshanetsky and A. M. Perelomov, Preprint ITEP-157, Moscow (1978).Google Scholar
  22. 22.
    I. M. Gel'fand and M. A. Naimark, “Unitary representations of the classical groups,” Tr. Mosk. Inst. Akad. Nauk SSSR,36 (1950).Google Scholar
  23. 23.
    A. A. Kirillov, Elements of the Theory of Representations [in Russian], Nauka (1972).Google Scholar
  24. 24.
    O. I. Bogoyavlensky, Commun. Math. Phys.,51, 201 (1976).Google Scholar
  25. 25.
    S. Helgason, Differential Geometry and Symmetric Spaces, New York (1962).Google Scholar
  26. 26.
    M. A. Ol'shanetskii and A. M. Perelomov, Preprint ITÉF-159 [in Russian], Moscow (1977).Google Scholar
  27. 27.
    B. Kostant, Preprint MIT (1979).Google Scholar

Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • M. A. Ol'shanetskii
  • A. M. Perelomov

There are no affiliations available

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