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

22 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

Access to Document

10.1016/j.na.2006.12.001

Cite this

@article{53427fcd476243b989b49a117df49185,

title = "A generalized Fitzhugh-Nagumo equation",

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.",

keywords = "Fitzhugh-Nagumo equation, Invertible mapping, Lie group method, Method of Lines",

author = "P. Browne and E. Momoniat and Mahomed, \{F. M.\}",

year = "2008",

month = feb,

day = "15",

doi = "10.1016/j.na.2006.12.001",

language = "English",

volume = "68",

pages = "1006--1015",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

issn = "0362-546X",

publisher = "Elsevier Ltd.",

number = "4",

}

TY - JOUR

T1 - A generalized Fitzhugh-Nagumo equation

AU - Browne, P.

AU - Momoniat, E.

AU - Mahomed, F. M.

PY - 2008/2/15

Y1 - 2008/2/15

N2 - 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.

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

UR - https://www.scopus.com/pages/publications/36749063849

U2 - 10.1016/j.na.2006.12.001

DO - 10.1016/j.na.2006.12.001

M3 - Article

AN - SCOPUS:36749063849

SN - 0362-546X

VL - 68

SP - 1006

EP - 1015

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 4

ER -

A generalized Fitzhugh-Nagumo equation

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this