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Nelin. Dinam., 2019, Volume 15, Number 1, Pages 13–19 (Mi nd636)  

Nonlinear physics and mechanics

On Integrability of the FitzHugh Rinzel Model

N. A. Kudryashov

Department of Applied Mathematics, National Research Nuclear University MEPHI, Kashirskoe sh. 31, Moscow, 115409 Russia

Abstract: The integrability of the FitzHugh Rinzel model is considered. This model is an example of the system of equations having the expansion of the general solution in the Puiseux series with three arbitrary constants. It is shown that the FitzHugh Rinzel model is not integrable in the general case, but there are two formal first integrals of the system of equations for its description. Exact solutions of the FitzHugh Rinzel system of equations are given.

Keywords: FitzHugh Rinzel model, Painlevé test, first integral, general solution, exact solution

Funding Agency Grant Number
Russian Science Foundation 18-11-00209
This research was supported by the Russian Science Foundation under Grant No 18-11-00209 Development of methods for investigation of nonlinear mathematical models.


DOI: https://doi.org/10.20537/nd190102

Full text: PDF file (191 kB)
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MSC: 37D40
Received: 03.03.2019
Accepted:17.03.2019
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Citation: N. A. Kudryashov, “On Integrability of the FitzHugh Rinzel Model”, Nelin. Dinam., 15:1 (2019), 13–19

Citation in format AMSBIB
\Bibitem{Kud19}
\by N. A. Kudryashov
\paper On Integrability of the FitzHugh Rinzel Model
\jour Nelin. Dinam.
\yr 2019
\vol 15
\issue 1
\pages 13--19
\mathnet{http://mi.mathnet.ru/nd636}
\crossref{https://doi.org/10.20537/nd190102}
\elib{http://elibrary.ru/item.asp?id=37293018}


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