Integrability conditions for an analogue of the relativistic Toda chain. (English. Russian original) Zbl 1121.37056

Theor. Math. Phys. 151, No. 1, 492-504 (2007); translation from Teor. Mat. Fiz. 151, No. 1, 66-80 (2007).
Summary: We consider a class of discrete-differential equations that contains the relativistic Toda chain and is characterized by one arbitrary function of six variables. We derive three conditions that allow testing the integrability of any given equation in this class. In deriving these conditions, we use higher symmetries distinguishing the equations that are integrable via the inverse scattering method.


37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems


higher symmetry
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