Skip to main content
SpringerLink
Log in

Nonlinear Poisson bracket, F-algebras, and noncommutative integration of linear differential equations

  • Elementary Particle Physics And Field Theory
  • Published:
Russian Physics Journal Aims and scope

Abstract

We study some properties of the nonlinear Poisson bracket and its analog for linear differential equations in partial derivatives (so-called F-algebras). We propose a method for noncommutative integration of linear differential equations for the case when the equation operator is embedded in an F-algebra. The method is based on the exact infinite irreducible representation of an F-algebra (λ-representation), which is introduced in the present paper.

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

Similar content being viewed by others

Literature cited

  1. V. G. Bagrov, D. M. Gitman, I. M. Ternov, et al., Exact Solutions to Relativistic Wave Equations [in Russian], Nauka, Novosibirsk (1982).

    Google Scholar 

  2. V. G. Bagrov, A. V. Shapovalov, and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 9, 19 (1991).

  3. A. V. Shapovalov and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 4, 95 (1991).

  4. A. V. Shapovalov and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 5, 33 (1991).

  5. V. G. Fedoseev, A. F. Shapovalov, and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 9, 43 (1991).

  6. M. V. Karasev and V. P. Maslov, The Nonlinear Poisson Bracket, Geometry and Quantization [in Russian], Nauka, Moscow (1991).

    Google Scholar 

  7. A. T. Fomenko, Symplectic Geometry, Methods and Applications, Izd. MGU, Moscow (1988).

    Google Scholar 

Download references

Authors
  1. A. V. Shapovalov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. V. Shirokov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

V. V. Kuibyshev Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 92–98, July, 1992.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shapovalov, A.V., Shirokov, I.V. Nonlinear Poisson bracket, F-algebras, and noncommutative integration of linear differential equations. Russ Phys J 35, 661–666 (1992). https://doi.org/10.1007/BF00559239

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00559239

Keywords

Search

Navigation