Theoretical and Mathematical Physics

, Volume 161, Issue 3, pp 1590–1598 | Cite as

The structure of polynomial conservation laws

  • R. N. Garifullin
  • A. B. Shabat


We consider periodic closures of integrable chains. We establish a compact formula for the generating function of the conservation laws. This generating function is common to classical integrable chains related to various second-order spectral problems. We study the stabilization problem for the form of the conservation laws in the limit as the closure period tends to infinity.


discrete equation conservation law chain 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Toda, Theory of Nonlinear Lattices (Springer Ser. Solid-State Sci., Vol. 20), Springer, Berlin (1981).zbMATHGoogle Scholar
  2. 2.
    R. I. Yamilov, Uspekhi Mat. Nauk, 38, No. 6(234), 155–156 (1983).MathSciNetGoogle Scholar
  3. 3.
    Yu. Mozer, Integrable Hamiltonian Systems and Spectral Theory [in Russian], RKhD, Izhevsk (1999).Google Scholar
  4. 4.
    V. E. Adler, V. G. Marikhin, and A. B. Shabat, Theor. Math. Phys., 129, 1448–1465 (2001).zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    A. P. Veselov and A. B. Shabat, Funct. Anal. Appl., 27, No. 2, 81–96 (1993).zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    V. E. Adler, Funct. Anal. Appl., 27, No. 2, 141–143 (1993).zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© MAIK/Nauka 2009

Authors and Affiliations

  1. 1.Institute of Mathematics with Computing Center, Ufa Science CenterRASUfaRussia
  2. 2.Landau Institute for Theoretical PhysicsRASChernogolovka, Moscow OblastRussia

Personalised recommendations