On some integrable lattice related by the Miura-type transformation to the Itoh-Narita-Bogoyavlenskii lattice

TL;DR

This paper demonstrates how the Itoh-Narita-Bogoyavlenskii lattice is connected to a differential-difference equation via a Miura-type transformation, providing explicit integrable hierarchies and analyzing Darboux transformations.

Contribution

It introduces a new connection between the Itoh-Narita-Bogoyavlenskii lattice and differential-difference equations through a Miura-type transformation, along with explicit integrable hierarchies and Darboux transformation analysis.

Findings

Establishment of a Miura-type transformation linking the lattices.

Explicit form of integrable hierarchies related to the lattice.

Analysis of elementary Darboux transformations for the modified equations.

Abstract

We show that by Miura-type transformation the Itoh-Narita-Bogoyavlenskii lattice, for any $n\geq 1$, is related to some differential-difference (modified) equation. We present corresponding integrable hierarchies in its explicit form. We study the elementary Darboux transformation for modified equations.