A generalized Fitzhugh-Nagumo equation

P. Browne; E. Momoniat; F. M. Mahomed

doi:10.1016/j.na.2006.12.001

A generalized Fitzhugh-Nagumo equation

P. Browne, E. Momoniat, F. M. Mahomed

University of the Witwatersrand

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

In this paper we investigate mappings of the classical Fitzhugh-Nagumo equation to a generalized Fitzhugh-Nagumo equation. These mappings are invertible and transform the solutions of the classical Fitzhugh-Nagumo equation into solutions of the generalized Fitzhugh-Nagumo equation considered here. These mappings are found by considering the Lie point symmetries admitted by the classical Fitzhugh-Nagumo equation and the generalized Fitzhugh-Nagumo equation considered here. A particular example of a generalized Fitzhugh-Nagumo equation that satisfies the boundary conditions of the classical Fitzhugh-Nagumo equation is considered. Numerical solutions of the generalized Fitzhugh-Nagumo equation that do not satisfy the boundary conditions of the classical Fitzhugh-Nagumo equation are obtained by implementing the Method of Lines.

Original language	English
Pages (from-to)	1006-1015
Number of pages	10
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	68
Issue number	4
DOIs	https://doi.org/10.1016/j.na.2006.12.001
Publication status	Published - 15 Feb 2008
Externally published	Yes

Keywords

Fitzhugh-Nagumo equation
Invertible mapping
Lie group method
Method of Lines

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2006.12.001

Cite this

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title = "A generalized Fitzhugh-Nagumo equation",

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AU - Browne, P.

AU - Momoniat, E.

AU - Mahomed, F. M.

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AB - In this paper we investigate mappings of the classical Fitzhugh-Nagumo equation to a generalized Fitzhugh-Nagumo equation. These mappings are invertible and transform the solutions of the classical Fitzhugh-Nagumo equation into solutions of the generalized Fitzhugh-Nagumo equation considered here. These mappings are found by considering the Lie point symmetries admitted by the classical Fitzhugh-Nagumo equation and the generalized Fitzhugh-Nagumo equation considered here. A particular example of a generalized Fitzhugh-Nagumo equation that satisfies the boundary conditions of the classical Fitzhugh-Nagumo equation is considered. Numerical solutions of the generalized Fitzhugh-Nagumo equation that do not satisfy the boundary conditions of the classical Fitzhugh-Nagumo equation are obtained by implementing the Method of Lines.

KW - Fitzhugh-Nagumo equation

KW - Invertible mapping

KW - Lie group method

KW - Method of Lines

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A generalized Fitzhugh-Nagumo equation

Abstract

Keywords

ASJC Scopus subject areas

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