New Solutions to a forced Huxley Equation Using a Family of Generalized Tanh Functions

Abstract

The tanh method devised by Malfiet is used to obtain analytic traveling wave solutions to nonlinear partial differential equations (PDEs) by employing a hyperbolic tangent ansatz. One such nonlinear PDE is the Huxley equation that demonstrates the electric behavior of the nerve axon to model nerve-impulse propagation. Previous studies have shown that the use of a Generalized Half-Angle Tanh (g-HATH) ansatz consisting of a family of tanh functions can generate new wave solutions when applied to a forced version of the PDE it is applied to. In this paper, the tanh method using the
g-HATH ansatz is applied to the forced Huxley Equation that allows for the derivation of new analytic kink solutions. Comparison of the original and new solutions for different p showed the reducibility of the new solutions to the original when p = 1, while decreasing p results in a decrease in kink wave height and various changes to the wave speed.