Advertisement

Ukrainian Mathematical Journal

, Volume 56, Issue 2, pp 198–207 | Cite as

Finite-Dimensional Nonlocal Reductions of the Inverse Korteweg–de Vries Dynamical System

  • O. V. Vorobiova
  • M. M. Prytula
Article
  • 16 Downloads

Abstract

We study finite-dimensional Moser-type reductions for the inverse nonlinear Korteweg–de Vries dynamical system and the Liouville integrability of these reductions in quadratures.

Keywords

Dynamical System Liouville Integrability Nonlocal 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    M. Prytula, V. Samoylenko, and U. Suyarov, "The complete integrability analysis of the inverse Korteweg-de Vries equation (inv KdV)," Nonlin. Vibration Probl. (Warsaw), 25, 411–422 (1993).Google Scholar
  2. 2.
    M. M. Prytula, A. K. Prykarpats'kyi, and I. V. Mykytyuk, Elements of the Theory of Differential-Geometric Structures and Dynamical Systems [in Ukrainian], UMK VO, Kiev (1988).Google Scholar
  3. 3.
    Yu. A. Mitropol'skii, N. N. Bogolyubov, Jr., A. K. Prikarpatskii, and V. G. Samoilenko, Integrable Dynamical Systems. Spectral and Differential-Geometric Aspects [in Russian], Naukova Dumka, Kiev (1987).Google Scholar
  4. 4.
    O. I. Bogoyavlenskii and S. P. Novikov, "On relationship between the Hamiltonian formalisms of stationary and nonstationary problems," Funct. Anal. Prilozhen., 10, No. 1, 9–13 (1976).Google Scholar
  5. 5.
    V. E. Zakharov, S. V. Manakov, S. P. Novikov, and A. P. Pitaevskii, Soliton Theory. Msethod of Inverse Problem [in Russian], Nauka, Moscow (1980).Google Scholar
  6. 6.
    A. Prykarpatsky, D. Blackmore, W. Strampp, Yu. Sydorenko, and R. Samuliak, "Some remarks on Lagrangian and Hamiltonian formalism," Condensed Matter Phys., No. 6, 79–104 (1995).Google Scholar
  7. 7.
    A. Prykarpatsky, O. Hentosh, M. Kopych, and R. Samuliak, "Neumann-Bogoliubov-Rosochatius oscillatory dynamical systems and their integrability via dual moment maps," J. Nonlin. Math. Phys., 2, No. 2, 98–113 (1995).Google Scholar
  8. 8.
    A. Prikarpatskii and I. V. Mikityuk, Algebraic Aspects of Integrability of Nonlinear Dynamical Systems on Manifolds [in Russian], Naukova Dumka, Kiev (1991).Google Scholar
  9. 9.
    P. A. M. Dirac, "Generalized Hamiltonian dynamics," Can. J. Math., 2, No. 2, 129–148 (1950).Google Scholar
  10. 10.
    F. Magri, "A simple model of the integrable Hamiltonian equation," J. Math. Phys., 19, No. 3, 1156–1162 (1978).Google Scholar

Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • O. V. Vorobiova
    • 1
  • M. M. Prytula
    • 1
  1. 1.Lviv National UniversityLviv

Personalised recommendations