Skip to main content
SpringerLink
Log in

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

  • Published:
Ukrainian Mathematical Journal Aims and scope

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  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. 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. 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. 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. V. E. Zakharov, S. V. Manakov, S. P. Novikov, and A. P. Pitaevskii, Soliton Theory. Msethod of Inverse Problem [in Russian], Nauka, Moscow (1980).

  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. 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. A. Prikarpatskii and I. V. Mikityuk, Algebraic Aspects of Integrability of Nonlinear Dynamical Systems on Manifolds [in Russian], Naukova Dumka, Kiev (1991).

  9. P. A. M. Dirac, "Generalized Hamiltonian dynamics," Can. J. Math., 2, No. 2, 129–148 (1950).

    Google Scholar 

  10. F. Magri, "A simple model of the integrable Hamiltonian equation," J. Math. Phys., 19, No. 3, 1156–1162 (1978).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lviv National University, Lviv

    O. V. Vorobiova & M. M. Prytula

Authors
  1. O. V. Vorobiova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. M. Prytula
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vorobiova, O.V., Prytula, M.M. Finite-Dimensional Nonlocal Reductions of the Inverse Korteweg–de Vries Dynamical System. Ukrainian Mathematical Journal 56, 198–207 (2004). https://doi.org/10.1023/B:UKMA.0000036096.08822.93

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:UKMA.0000036096.08822.93

Keywords

Search

Navigation