Recursion operator of the Narita-Itoh-Bogoyavlensky lattice

TL;DR

This paper constructs a recursion operator for the Narita-Itoh-Bogoyavlensky lattice, revealing its symmetries and bi-Hamiltonian structures, and demonstrates its ability to generate numerous local symmetries.

Contribution

It introduces a new recursion operator for the lattice, derived from its Lax representation, and explores its symmetry and Hamiltonian properties.

Findings

Recursion operator successfully generates infinite local symmetries.

The lattice possesses bi-Hamiltonian structures.

The recursion operator is highly nonlocal but produces local symmetries.

Abstract

We construct a recursion operator for the family of Narita-Itoh-Bogoyavlensky infinite lattice equations using its Lax presentation and present their mastersymmetries and bi-Hamiltonian structures. We show that this highly nonlocal recursion operator generates infinite many local symmetries.