Ukrainian Mathematical Journal

, Volume 40, Issue 4, pp 351–356 | Cite as

Subalgebras of the poincaré algebra AP(2, 3) and the symmetric reduction of the nonlinear ultrahyperbolic d'Alembert equation. I

  • L. F. Barannik
  • V. I. Lagno
  • V. I. Fushchich


Symmetric Reduction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    V. I. Fushchich, “Symmetry in problems of mathematical physics,” in: Theoretical-Algebraic Methods of Research in Mathematical Physics [in Russian], Inst. Mat. Akad. Nauk UkrSSR, Kiev (1981), pp. 6–28.Google Scholar
  2. 2.
    V. I. Fushchich and N. I. Serov, “The symmetry and some exact solutions of the nonlinear many-dimensional Liouville, d'Alembert, and eikonal equations,” J. Phys. A,16, No. 15, 3645–3656 (1983).Google Scholar
  3. 3.
    V. G. Kadyshevskii, “A new approach to the theory of electromagnetic interactions,” Fiz. Elementar. Chastits At. Yad.,11, No. 1, 5–36 (1980).Google Scholar
  4. 4.
    V. I. Fushchich, “Representations of the complete nonhomogeneous de Sitter group and equations in the five-dimensional approach,” Teor. Mat, Fiz.,4, No. 3, 360–382 (1970).Google Scholar
  5. 5.
    V. I. Fushchich, “On the symmetry and exact solutions of multidimensional nonlinear wave equations,” Ukr. Mat. Zh.,39, No. 1, 116–123 (1987).Google Scholar
  6. 6.
    L. V. Ovsyannikov, Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978).Google Scholar
  7. 7.
    A. M. Grundland, J. Harnad, and P. Winternitz, “Symmetry reduction for nonlinear relativistically invariant equations,” J. Math. Phys.,25, No. 4, 791–806 (1984).Google Scholar
  8. 8.
    J. Patera, P. Winternitz, and H. Zassenhaus, “Continuous subgroups of the fundamental groups of physics. I. General method and the Poincaré group,” J. Math. Phys.,16, No. 8, 1597–1624 (1975).Google Scholar
  9. 9.
    J. Patera, P. Winternitz, and H. Zassenhaus, “Quantum numbers for particles in de Sitter space,” J. Math. Phys.,17, No. 5, 717–728 (1976).Google Scholar
  10. 10.
    V. I. Fushchich, A. F. Barannik, L. F. Barannik, and V. M. Fedorchuk, “Continuous subgroups of the Poincaré group P(1, 4),” J. Phys. A,18, No. 14, 2893–2899 (1985).Google Scholar
  11. 11.
    L. F. Barannik, V. I. Lagno, and V. I. Fushchich, “Subalgebras of the generalized Poin-caré algebra AP(2, n),” Akad. Nauk UkrSSR, Inst. Mat., Preprint, No. 89 (1985).Google Scholar
  12. 12.
    L. F. Barannik and V. I. Fushchich, “On subalgebras of the Lie algebra of the extended Poincaré group ¯P(1, n),” J. Math. Phys.,28, No. 7, 1003–1017 (1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • L. F. Barannik
    • 1
  • V. I. Lagno
    • 1
  • V. I. Fushchich
    • 1
  1. 1.Institute of MathematicsAcademy of Sciences of the Ukrainian SSRKiev

Personalised recommendations