Russian Physics Journal

, Volume 35, Issue 11, pp 1031–1036 | Cite as

Noncommutative integration of quantum Euler equations on the Lie algebraso (4)

  • Ya. V. Lisitsyn
  • A. V. Shapovalov
  • I. V. Shirokov
Elementary Particle Physics And Field Theory
  • 14 Downloads

Abstract

The quantum analogue is considered of the classical Euler equations on the Lie algebraso (4) for the integrable case. With the help of the method of non-commutative integration (A. V. Shapovalov, I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 4, p. 95; No. 5, p. 33 (1991)) and the method of separation of variables, the quantum equations are reduced to the solution of a system of ordinary differential equations.

Keywords

Differential Equation Ordinary Differential Equation Euler Equation Integrable Case Quantum Analogue 

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Literature cited

  1. 1.
    V. N. Shapovalov, Sib. Mat. Zh.,20, No. 5, 1117–1130 (1979).Google Scholar
  2. 2.
    A. S. Mishchenko and A. T. Fomenko, Funkts. Anal. Prilozhen.,12, No. 2, 46–56 (1978).Google Scholar
  3. 3.
    A. S. Mischenko and A. T. Fomenko, Tr. Sem. Vekt. Tenz. Anal., No. 20, 5–54 (1981).Google Scholar
  4. 4.
    M. Mozer, Usp. Mat. Nauk,36, No. 6, 109–151 (1981).Google Scholar
  5. 5.
    V. N. Shapovalov, Differents. Uravn.,16, No. 10, 1864–1874 (1980).Google Scholar
  6. 6.
    I. V. Komarov and V. B. Kuznetsov, Zap. Nauch. Sem. LOMI,164, 134–141 (1987).Google Scholar
  7. 7.
    V. B. Kuzetsov and A. V. Tsiganov, J. Phys. A,22, L73-L79 (1989).Google Scholar
  8. 8.
    A. T. Fomenko, Sympletic Geometry. Methods and Applications [in Russian], Moscow State University, Moscow (1988).Google Scholar
  9. 9.
    A. V. Shapovalov and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 4, 95–100 (1991).Google Scholar
  10. 10.
    A. V. Shapovalov and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 5, 33–38 (1991).Google Scholar
  11. 11.
    A. P. Veselov, Dokl. Akad. Nauk SSSR, 276, No. 3, 590–593 (1984).Google Scholar
  12. 12.
    V. G. Bagrov, B. F. Samsonov, A. V. Shapovalov, and I. V. Shirokov, Preprint No. 27, Theoretical Department of the Siberian Branch of the Academy of Sciences of the USSR, Tomsk (1990).Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • Ya. V. Lisitsyn
  • A. V. Shapovalov
  • I. V. Shirokov

There are no affiliations available

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