Abstract
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 simulation.
Highlights
Studies of traveling wave (TW) solutions to nonlinear evolution equations attract attention of many researchers
The subject of this work is a study of the solitary wave solutions supported by the modification of the FitzHugh–Nagumo equations [8, 20] taking into account the effects of relaxation
The main problem we address in this work is the proof of existence of the solitary waves among the set of TW solutions of the modified FitzHugh–Nagumo system
Summary
Studies of traveling wave (TW) solutions to nonlinear evolution equations attract attention of many researchers. The subject of this work is a study of the solitary wave solutions supported by the modification of the FitzHugh–Nagumo equations [8, 20] taking into account the effects of relaxation. Equation (14) differs from the first equation of system (3) by the presence of an additional factors at the term vt As it was noted in the introduction, the main purpose of this paper is to rigorously prove the existence of a soliton solution for a hyperbolic analogue of the FitzHugh–Nagumo system. It is worth noting that numerical experiments confirm the presence of soliton regimes among the solutions of system (14)–(15), the rigorous proof of their existence is beyond the scope of this paper
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