A relaxation wave solution of the FitzHugh-Nagumo equations
For the system of FitzHugh-Nagumo equations and certain values of parameters, there exists a relaxation wave solution: a moving spatially periodic structure for which one of the dependent variables has intervals of slow and fast changes within its period. An asymptotic expansion for the solution is constructed (as a power series in the small parameter ε) consisting of regular terms and transition layers. Along with the asymptotic expansion, the velocity of the structure, its period, and the distance between “jumps” of one of the functions are determined.