Discrete Toda Field Equations

Abstract

There are two-dimensional Toda field equations corresponding to each (finite or affine) Lie algebra. The question addressed in this note is whether there exist integrable discrete versions of these. It is shown that for certain algebras (such as $A_n$, $A_n^{(1)}$ and $B_n$) there do, but some of these systems are defined on the half-plane rather than the full two-dimensional lattice.

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Cited by in corpus (10)

• Geometric Discretisation of the Toda System
• Pfaffian and Determinant Solutions to A Discretized Toda Equation for $B_r,C_r$ and $D_r$
• On Darboux integrability of discrete 2D Toda lattices
• Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time
• Discretization of hyperbolic type Darboux integrable equations preserving integrability
• Cartan matrices and integrable lattice Toda field equations
• Lax Pairs for Integrable Lattice Systems
• Solutions of Discretized Affine Toda Field Equations for A_{n}^{(1)}, B_{n}^{(1)}, C_{n}^{(1)}, D_{n}^{(1)}, A_{n}^{(2)} and D_{n+1}^{(2)}
• Integral preserving discretization of 2D Toda lattices
• Finite-dimensional reductions of the discrete Toda chain