On some class of homogeneous polynomials and explicit form of integrable hierarchies of differential-difference equations

TL;DR

This paper introduces two classes of homogeneous polynomials that are instrumental in constructing integrable hierarchies for certain lattice systems, advancing the understanding of their algebraic structure.

Contribution

It presents new classes of homogeneous polynomials and demonstrates their application in deriving integrable hierarchies for specific differential-difference equations.

Findings

New classes of homogeneous polynomials introduced.

Explicit construction of integrable hierarchies for lattice systems.

Enhanced understanding of algebraic structures in integrable systems.

Abstract

We introduce two classes of homogeneous polynomials and show their role in constructing of integrable hierarchies for some integrable lattices.