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Finite-Dimensional Discrete Systems Integrated in Quadratures

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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.

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  1. Sterlitamak State Pedagogical Institute, Sterlitamak, Bashkortostan, Russia

    T. G. Kazakova

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  1. T. G. Kazakova
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Kazakova, T.G. Finite-Dimensional Discrete Systems Integrated in Quadratures. Theoretical and Mathematical Physics 138, 356–369 (2004). https://doi.org/10.1023/B:TAMP.0000018452.62337.c8

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  • DOI: https://doi.org/10.1023/B:TAMP.0000018452.62337.c8

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