Skip to main content
SpringerLink
Log in

Quantum lie algebra of currents — The universal algebraic structure of symmetries of completely integrable dynamical systems

  • Published:
Ukrainian Mathematical Journal Aims and scope

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.

Institutional subscriptions

Literature cited

  1. N. N. Bogolyubov and N. N. Bogolyubov Jr., Introduction to Quantum Statistical Mechanics [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  2. N. N. Bogolyubov Jr. and A. K. Prikarpatskii, “The N. N. Bogolyubov quantum method of generating functionals in statistical physics,” Ukr. Mat. Zh.,38, No. 3, 285–289 (1986).

    Google Scholar 

  3. B. N. Fil' and A. K. Prikarpatskii, “Representations of the Lie algbera of currents on S1 associated with integral dynamical systems,” Dokl. Akad. Nauk SSSR,298, No. 3, 1021–1024 (1986).

    Google Scholar 

  4. N. N. Bogolyubov Jr. and A. K. Prikarpatskii, “The Bogolyubov quantum method of generating functionals in statistical physics,” Elementarnye Chastitsy At. Yad.,17, No. 4, 789–827 (1986).

    Google Scholar 

  5. V. G. Samoilenko and A. K. Prikarpatskii, “Algebraic structure of the gradient method in the investigations of dynamical systems,” Preprint Akad. Nauk Ukr. SSR, Inst. Math., No. 86-52, Kiev (1986).

  6. A. K. Prikarpatskii, “Gradient method of the construction of criteria of the integrability of dynamical systems,” Dokl. Akad. Nauk SSSR,287, No. 4, 827–832 (1986).

    Google Scholar 

  7. Yu. A. Mitropol'skii, V. G. Samoilenko, and A. K. Prikarpatskii, “An asymptotic method of construction of implectic and recursive operators of integrable dynamical systems,” ibid., No. 6, 1312–1317 (1986).

    Google Scholar 

  8. A. Fokas and B. Fucssteiner, “Bäcklund transformations hereditary symmetries,” Physica, Ser. D.,4, No. 1, 47–66 (1981).

    Google Scholar 

  9. V. K. Mel'nikov, “Some new nonlinear evolution equations integrable by the inverse problem method,” Mat. Sb.,49, No. 2, 461–489 (1984).

    Google Scholar 

  10. D. Kaup and A. C. Newell, “An exact solution for a derivative nonlinear Schrödinger equation,” J. Math. Phys.,19, No. 4, 798–801 (1987).

    Google Scholar 

  11. A. K. Prikarpatskii and N. N. Bogolyubov Jr., “Complete integrability of nonlinear systems of the hydrodynamical type,” Teor. Mat. Fiz.,67, No. 3, 410–425 (1987).

    Google Scholar 

  12. N. N. Bogolyubov Jr., A. M. Kurbatov, A. K. Prikarpatskii, and V. G. Samoilenko, “A nonlinear model of the Schrödinger type,” ibid.,65, No. 2, 271–284 (1985).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Problems of Applied Mechanics and Mathematics, Academy of Sciences of the Ukrainian SSR, Lvov

    B. N. Fil', A. K. Prikarpatskii & N. N. Pritula

Authors
  1. B. N. Fil'
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. K. Prikarpatskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. N. Pritula
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 40, No. 6, pp. 764–768, November–December, 1988.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fil', B.N., Prikarpatskii, A.K. & Pritula, N.N. Quantum lie algebra of currents — The universal algebraic structure of symmetries of completely integrable dynamical systems. Ukr Math J 40, 645–649 (1988). https://doi.org/10.1007/BF01057184

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01057184

Keywords

Search

Navigation