This article is cited in 5 papers

Finite-Dimensional Discrete Systems Integrated in Quadratures

T. G. Kazakova

Sterlitamak State Pedagogical Institute

Abstract: We consider finite-dimensional reductions (truncations) of discrete systems of the type of the Toda chain with discrete time that retain the integrability. We show that for finite-dimensional chains, in addition to integrals of motion, we can construct a rich family of higher symmetries described by the master symmetry. We reduce the problem of integrating a finite-dimensional system to the implicit function theorem.

Keywords: integrability, truncation condition, zero-curvature equation, classical symmetry, master symmetry, integrals of motion.

Received: 04.04.2003

DOI: 10.4213/tmf30

 English version: Theoretical and Mathematical Physics, 2004, 138:3, 356–369

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