Existence of the solitary wave solutions supported by the modified FitzHugh–Nagumo system

We study a system of nonlinear differential equations simulating transport phenomena in active media. The model we are interested in is a generalization of the celebrated FitzHugh–Nagumo system describing the nerve impulse propagation in axon. The modeling system is shown to possesses soliton-like solutions under certain restrictions on the parameters. The results of theoretical studies are backed by the direct numerical...