Oğul Esen, Anindya Ghose Choudhury, Partha Guha, “On integrals, Hamiltonian and metriplectic formulations of polynomial systems in 3D”, Theor. Appl. Mech., 2017, Volume 44, Issue 1,Pages <nobr>15

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On integrals, Hamiltonian and metriplectic formulations of polynomial systems in 3D

Oğul Esen^a, Anindya Ghose Choudhury^b, Partha Guha^c

^a Department of Mathematics, Gebze Technical University, Gebze-Kocaeli, Turkey
^b Department of Physics, Surendranath College, Calcutta, India
^c SN Bose National Centre for Basic Sciences, Salt Lake, Kolkata, India

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.

Keywords: Darboux integrability method, the reduced three-wave interaction problem, Rabinovich system, Hindmarsh–Rose model, oregonator model, metriplectic Structure, Nambu-Poisson brackets.

MSC: 37K10, 70G45

Received: 18.11.2016
Revised: 23.02.2017

Language: English

DOI: 10.2298/TAM161118001E