A generalized Fitzhugh-Nagumo equation

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. (C) 2007 Elsevier Ltd. All rights reserved.