We are interested in various types of localized waves in FitzHugh-Nagumo equations. Variational methods have been successfully worked out to establish the existence of traveling and standing waves. Starting with a simple planar traveling front, an ordered method is employed to demonstrate different front propagation between two stable equilibria. If these two stable equilibria are in the same energy level, a saddle-focus condition ensures that there are infinite number of standing waves with multiple fronts.
"Localized Front Structures in FitzHugh-Nagumo Equations." Taiwanese J. Math. 23 (2) 333 - 349, April, 2019. https://doi.org/10.11650/tjm/181112