Cartan matrices and integrable lattice Toda field equations

Details Cartan matrices and integrable lattice Toda field equations Cartan matrices and integrable lattice Toda field equations

2011-05-23

arxiv.org/abs/1105.4446v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

21 pages

Scientific paper

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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