Finite-dimensional reductions of the discrete Toda chain

Abstract

The problem of construction of integrable boundary conditions for the discrete Toda chain is considered. The restricted chains for properly chosen closure conditions are reduced to the well known discrete Painlevé equations $d{P}_{III}$, $d{P}_V$, $d{P}_{VI}$. Lax representations for these discrete Painlevé equations are found.

Submitted to Jornal of Physics A: Math. Gen., 14 pages

References in corpus (4)

• Quantum Integrable Systems and Elliptic Solutions of Classical Discrete Nonlinear Equations
• Discrete Painleve equations: coalescences, limits and degeneracies
• Discrete Toda Field Equations
• Integrable boundary conditions for the Toda lattice