Cartan matrices and integrable lattice Toda field equations

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 $A_2$, $B_2$, $C_2$, $G_2$ 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 $D_N^{(2)}$ the corresponding systems are supplied with the Lax representation.

21 pages

References in corpus (4)

• T-systems and Y-systems in integrable systems
• Characteristic Lie Algebra and Classification of Semi-Discrete Models
• On Darboux Integrable Semi-Discrete Chains
• Discretization of hyperbolic type Darboux integrable equations preserving integrability

Cited by in corpus (6)

• On Darboux integrability of discrete 2D Toda lattices
• Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time
• Characteristic Lie Algebras of Integrable Differential-Difference Equations in 3D
• Integral preserving discretization of 2D Toda lattices
• Semidiscrete Toda lattices
• Affine Lie algebras, Lax pairs and integrable discrete and continuous systems