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Approximate Closed-form Solutions for the Rabinovich System via the Optimal Auxiliary Functions Method
Version 1
: Received: 26 September 2022 / Approved: 30 September 2022 / Online: 30 September 2022 (10:59:49 CEST)
A peer-reviewed article of this Preprint also exists.
Ene, R.-D.; Pop, N.; Lapadat, M. Approximate Closed-Form Solutions for the Rabinovich System via the Optimal Auxiliary Functions Method. Symmetry 2022, 14, 2185. Ene, R.-D.; Pop, N.; Lapadat, M. Approximate Closed-Form Solutions for the Rabinovich System via the Optimal Auxiliary Functions Method. Symmetry 2022, 14, 2185.
Abstract
Based on some geometrical properties of the Rabinovich system the closed-form solutions of the equations has been established. Moreover the Rabinovich system is reduced to a nonlinear differential equation depending on an auxiliary unknown function. The approximate analytical solutions are built using the Optimal Auxiliary Functions Method (OAFM). A good agreement between the analytical and corresponding numerical results has been performed. The accuracy of the obtained results emphasizes that this procedure could be successfully applied for more dynamical systems with these geometrical properties.
Keywords
optimal auxiliary functions method; Rabinovich system; symmetries; Hamilton--Poisson realization; periodical orbits
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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