## Abstract

We consider a perturbation of the Fitzhugh-Nagumo equation. The perturbation is proportional to the electric potential across the cell membrane. The purpose of this investigation is to determine the effects of a change in electric potential across the cell membrane. Exact solutions of the perturbed equation are easily obtained from the well-known solutions of the unperturbed Fitzhugh-Nagumo equation. The method of approximate conditional symmetries is used to obtain first-order approximate solutions of the perturbed Fitzhugh-Nagumo equation. The approximate solutions are compared with the exact solutions of the perturbed equation. The exact solutions of the perturbed equation do not indicate a change in the wave front connecting one constant state to another. There is only a proportional increase or decrease in the constant nonzero state. The approximate solutions do show a change in the shape of the wave front connecting two constant states as well as a proportional increase or decrease in the constant nonzero state.

Original language | English |
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Article number | 023503 |

Journal | Journal of Mathematical Physics |

Volume | 46 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 2005 |

Externally published | Yes |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics