On complete integrability of the Mikhailov-Novikov-Wang system

TL;DR

This paper proves the complete integrability of a new two-component fifth-order system by establishing its Hamiltonian and symplectic structures, recursion operator, and infinite symmetries, linking it to known integrable equations.

Contribution

It introduces compatible Hamiltonian and symplectic structures for the system, demonstrating its complete integrability and connection to the Kaup--Kupershmidt equation.

Findings

Existence of compatible Hamiltonian and symplectic structures

Presence of a hereditary recursion operator

Infinite symmetries and conservation laws

Abstract

We obtain compatible Hamiltonian and symplectic structure for a new two-component fifth-order integrable system recently found by Mikhailov, Novikov and Wang (arXiv:0712.1972), and show that this system possesses a hereditary recursion operator and infinitely many commuting symmetries and conservation laws, as well as infinitely many compatible Hamiltonian and symplectic structures, and is therefore completely integrable. The system in question admits a reduction to the Kaup--Kupershmidt equation.