Differential-difference integrable exponential-type systems are studied corresponding to the Cartan matrices of semi-simple or affine Lie algebras. For the systems corresponding to the algebras A 2 , B 2 , C 2 , G 2 , the complete sets of integrals in both directions are found. For the simple Lie algebras of the classical series A N , B N , C N and affine algebras of series D (2) N , the corresponding systems are supplied with the Lax representation.
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Habibullin et al. (2011) studied this question.
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