Semidiscrete Toda lattices

TL;DR

This paper investigates integrable boundary conditions for semidiscrete Toda lattices, introduces a Lax representation for the C-series, and classifies compatible cut-off constraints using nonlocal variables and symmetries.

Contribution

It provides the first Lax representation for the semidiscrete C-series Toda lattice and classifies integrable cut-off constraints compatible with lattice symmetries.

Findings

Lax presentation for semidiscrete C-series Toda lattice obtained

Classification of compatible cut-off constraints achieved

Nonlocal variables used to express symmetries

Abstract

Integrable cut-off constraints for semidiscrete Toda lattice are studied in this paper. Lax presentation for semidiscrete analog of the $C$-series Toda lattice is obtained. Nonlocal variables that allow to express symmetries of the infinite semidiscrete lattice are introduced and cut-off constraints or a certain type compatible with symmetries of the infinite lattice are classified.