ON INTEGRALS, HAMILTONIAN AND METRIPLECTIC FORMULATIONS OF POLYNOMIAL SYSTEMS IN 3D

Abstract

The first integrals of the reduced three-wave interaction problem, the Rabinovich system, the Hindmarsh-Rose model, and the Oregonator model are derived using the method of Darboux polynomials. It is shown that, the reduced three-wave interaction problem, the Rabinovich system, the Hindmarsh-Rose model can be written in a bi-Hamiltonian/ Nambu metriplectic form.