Orlando Ragnisco ; Federico Zullo - The N-species integrable Volterra system as a maximally superintegrable Hamiltonian system

ocnmp:15714 - Open Communications in Nonlinear Mathematical Physics, June 10, 2025, Volume 5 - https://doi.org/10.46298/ocnmp.15714
The N-species integrable Volterra system as a maximally superintegrable Hamiltonian systemArticle

Authors: Orlando Ragnisco ; Federico Zullo

    The results presented in this paper are a natural development of those described in the paper {\it The Volterra Integrable case. Novel analytical and numerical results} (OCNMP Vol.4 (2024) pp 188-211), where the authors reconsidered the integrable case of the Hamiltonian $N$-species Lotka-Volterra system, introduced by Vito Volterra in 1937. There, an alternative approach for constructing the integrals of motion has been proposed, and compared with the old Volterra approach. Here we go beyond, and show that in fact the model introduced by Volterra and studied by us is not just integrable, but is maximally superintegrable and reducible to a system with only one degree of freedom regardless the number of species considered. We present both analytical and numerical results.


    Volume: Volume 5
    Published on: June 10, 2025
    Accepted on: May 27, 2025
    Submitted on: May 20, 2025
    Keywords: Nonlinear Sciences - Exactly Solvable and Integrable Systems

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