A variational approach for novel solitary solutions of FitzHugh-Nagumo equation arising in the nonlinear reaction-diffusion equation

Purpose In the nonlinear model of reaction-diffusion, the Fitzhugh-Nagumo equation plays a very significant role. This paper aims to generate innovative solitary solutions of the Fitzhugh-Nagumo equation through the use of variational formulation. Design/methodology/approach The partial differential equation of Fitzhugh-Nagumo is modified by the appropriate wave transforms into a dimensionless nonlinear ordinary differential equation, which is solved by a semi-inverse variational method. Findings This paper uses a variational approach to the Fitzhugh-Nagumo equation developing new solitary solutions. The condition for the continuation of new solitary solutions has been met. In addition, this paper sets out the Fitzhugh-Nagumo equation fractal model and its variational principle. The findings of the solitary solutions have shown that the suggested method is very reliable and efficient. The suggested algorithm is very effective and is almost ideal for use in such problems. Originality/value The Fitzhugh-Nagumo equation is an important nonlinear equation for reaction-diffusion and is typically used for modeling nerve impulses transmission. The Fitzhugh-Nagumo equation is reduced to the real Newell-Whitehead equation if beta = -1. This study provides researchers with an extremely useful source of information in this area.