Theoretical and Mathematical Physics

, Volume 115, Issue 3, pp 639–646 | Cite as

First integrals of generalized Toda chains

  • V. É. Adler
  • A. B. Shabat


We construct a zero-curvature representation for generalzed Toda chains. Evaluating the first integrals amounts to multiplying the matrices that depend linearly on the fields and satisfy a given multiplication table.


Commutation Relation Poisson Bracket Multiplication Table Toda Chain Concrete Matrix 
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.
    V. É. Adler and A. B. Shabat,Theor. Math. Phys.,111, 647 (1997).zbMATHMathSciNetGoogle Scholar
  2. 2.
    V. É. Adler and A. B. Shabat,Theor. Math. Phys.,112, 935 (1997).zbMATHMathSciNetGoogle Scholar
  3. 3.
    Yu. B. Suris,J. Phys. A,29, 451 (1996).zbMATHCrossRefADSMathSciNetGoogle Scholar
  4. 4.
    V. É. Adler and I. T. Khabibullin,Funct. Anal. Appl.,31, 75 (1997).zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    V. É. Adler and R. I. Yamilov,J. Phys. A,27, 477 (1994).zbMATHCrossRefADSMathSciNetGoogle Scholar
  6. 6.
    R. I. Yamilov, “Classification of Toda type scalar lattices,” in:Proceedings of the International Workshop NEEDS'92, World Scientific, Singapore (1993), p. 423.Google Scholar
  7. 7.
    A. B. Shabat and R. I. Yamilov,Leningrad Math. J.,2, 377 (1991).zbMATHMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • V. É. Adler
    • 1
  • A. B. Shabat
    • 2
  1. 1.Institute for Mathematics, Ufa Science CenterRussian Academy of SciencesUfaRussia
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow RegionRussia

Personalised recommendations