On some class of reductions for Itoh-Narita-Bogoyavlenskii lattice

TL;DR

This paper explores a broad class of constraints compatible with the Itoh-Narita-Bogoyavlenskii lattice hierarchy, expressing them as discrete conservation laws involving polynomial functions.

Contribution

It introduces a new class of constraints for the lattice hierarchy, formulated as discrete conservation laws with polynomial functions, expanding understanding of integrable lattice systems.

Findings

Identifies a broad class of compatible constraints.

Expresses constraints as discrete conservation laws.

Provides a framework for polynomial discrete functions.

Abstract

We show a broad class of constraints compatible with Itoh-Narita-Bogoyavlenskii lattice hierarchy. All these constraints can be written in the form of discrete conservation law $I_{i+1}=I_i$ with appropriate homogeneous polynomial discrete function $I=I[a]$.