Approximate conditional symmetries and approximate solutions of the perturbed Fitzhugh-Nagumo equation

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. (C) 2005 American Institute of Physics.