Monostable-Type Travelling Wave Solutions of the Diffusive FitzHugh-Nagumo-Type System in R N

Abstract

This paper is concerned with monostable-type travelling wave solutions of the diffusive FitzHugh-Nagumo-type system (FHN) in ${\mathbf{R}}^N$ for the two components $u$ and $v$. By solving $v$ in terms of $u$, this system can be reduced to a nonlocal single equation for $u$. When the diffusion coefficients in the system are equal, we construct travelling wave solutions for the non-local equation by the method of super- and subsolutions developed by Morita and Ninomiya (2008) Moreover, we propose a condition for $\gamma$, which is similar to the condition Reinecke and Sweers (1999) used to transform (FHN) into a quasimonotone system.