Some new integrable systems of two-component fifth order equations

TL;DR

This paper introduces four new fifth-order integrable coupled systems with seventh-order symmetry, providing their recursion operators and bi-Hamiltonian structures, and investigates their integrability.

Contribution

It develops four novel fifth-order integrable coupled systems with symmetry and explores their recursion operators and Hamiltonian structures.

Findings

Four new integrable systems are established.

Recursion operators and bi-Hamiltonian formulations are provided for some systems.

The integrability of the systems is confirmed.

Abstract

In this work we develop some fifth-order integrable coupled systems of weight $0$ and $1$ which possess seventh-order symmetry. We establish four new systems, where in some cases, related recursion operator and bi-Hamiltonian formulations are given. We also investigate the integrability of the developed systems.