Abstract
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 A2, B2, C2, G2, the complete sets of integrals in both directions are found. For the simple Lie algebras of the classical series AN, BN, CN and affine algebras of series D(2)N, the corresponding systems are supplied with the Lax representation.
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