On solutions for some class of integrable difference equations

TL;DR

This paper demonstrates that solutions to certain ordinary difference equations can be extended to a hierarchy of integrable difference equations, exemplified by solutions related to second-order linear recursions with periodic coefficients.

Contribution

It introduces a method to generate solutions for a hierarchy of integrable difference equations from solutions of a single ordinary difference equation.

Findings

Any solution of a given ordinary difference equation can solve a hierarchy of integrable difference equations.

Provides an example involving solutions related to second-order linear recursions with 2-periodic coefficients.

Establishes a connection between simple recursions and complex integrable systems.

Abstract

In this paper we show that an arbitrary solution of one ordinary difference equation is also a solution for a hierarchy of integrable difference equations. We also provide an example of such a solution that is related to sequence generated by a second-order linear recursion with 2-periodic coefficients.