Theoretical and Mathematical Physics

, Volume 103, Issue 3, pp 701–705 | Cite as

On third Poisson structure of KdV equation

  • A. Gorsky
  • A. Marshakov
  • A. Orlov
  • V. Rubtsov


The third Poisson structure of the KdV equation in terms of canonical “free fields” and the reduced WZNW model is discussed. We prove that it is “diagonalized” in the Lagrange variables which were used before in the formulation of 2d gravity. We propose a quantum path integral for the KdV equation based on this representation.


Poisson Structure Free Field Lagrange Variable WZNW Model Quantum Path 
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.


  1. 1.
    F. Magri,J. Math. Phys.,19, 1156–1162 (1978).Google Scholar
  2. 2.
    B. Enriques, A. Orlov, and V. Rubtsov,JETP Lett., No. October 1993.Google Scholar
  3. 3.
    A. Alekseev and S. Shatashvili,Nucl. Phys.,B329, 719 (1989).Google Scholar
  4. 4.
    A. Polyakov,Mod. Phys. Lett.,A2, 893 (1987).Google Scholar
  5. 5.
    V. Knizhnik, A. Polyakov, and A. Zamolodchikov,Mod. Phys. Lett.,A3, 819 (1988).Google Scholar
  6. 6.
    V. Drinfeld and V. Sokolov,J. Sov. Math.,30, 1975–2036 (1985).Google Scholar
  7. 7.
    V. Fateev and S. Lukyanov,Int. J. Mod. Phys.,A3, 507 (1988);A7 (1992).Google Scholar
  8. 8.
    S. Lukyanov,Funct. Anal. Appl.,22, 1 (1988).Google Scholar
  9. 9.
    G. Wilson,Phys. Lett.,A132, 445 (1988).Google Scholar
  10. 10.
    E. Arbarello, C. de Koncini, V. Kac, and G. Procesi,Commun. Math. Phys.,117, 1 (1988).Google Scholar
  11. 11.
    A. Gorsky,Yad. Fiz. (1991).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • A. Gorsky
    • 1
  • A. Marshakov
    • 1
  • A. Orlov
    • 1
  • V. Rubtsov
    • 1
  1. 1.Institute of Theoretical PhysicsMoscowRussia

Personalised recommendations