Meromorphic solutions in the Fitzhugh-Nagumo model
type: Item
instance of: scholarly article
title: Meromorphic solutions in the Fitzhugh-Nagumo model
zbMATH Open document ID: 1394.34184
author: Maria V. Demina
author: Nikolai A. Kudryashov
published in: Applied Mathematics Letters
publication date: 2018-06-20T00:00:00Z
review text: The system of Fitz-Nagumo differential equations \[ (1) \quad v_t=v-v^3 - u+\sigma, \quad \tau u_t=v-\beta u-\alpha, \quad \alpha , \beta, \sigma, \tau \in C \] is considered in the paper. For this system the authors presented two new transcendental solutions. These solutions are obtained as a result of the description of all meromorphic solutions of the auxiliary equation \[ 2\tau ww_{tt}-\tau w_t^2+2\{3 \tau w^2+(\beta-\tau )w\}w_t+4\beta w^3+4(1-\beta)w^2=0 \] associated with the system (1) for certain values of parameters.
Mathematics Subject Classification ID: 34M05
zbMATH DE Number: 6891851
zbMATH Keywords: FitzHugh-Nagumo model
zbMATH Keywords: meromorphic solution
zbMATH Keywords: complex differential equation
zbMATH Keywords: Nevalinna theory
zbMATH Keywords: local alysis
reviewed by: Mykola Grygorenko
MaRDI profile type: Publication
full work available at URL: j.aml.2018.02.012
OpenAlex ID: W2792500597
cites work: Q5723337
cites work: On Integral and Meromorphic Functions
cites work: Q5441098
cites work: Explicit expressions for meromorphic solutions of autonomous nonlinear ordinary differential equations
cites work: From Laurent series to exact meromorphic solutions: The Kawahara equation
cites work: On elliptic solutions of nonlinear ordinary differential equations
cites work: Elliptic solutions in the Hénon-Heiles model
cites work: Q3151170
cites work: Analytical properties of nonlinear dislocation equation
cites work: Analytical properties of the perturbed FitzHugh-Nagumo model
DOI: 10.1016/J.AML.2018.02.012
description: scientific article; zbMATH DE number 6891851