Meromorphic solutions in the FitzHugh-Nagumo model

The FitzHugh-Nagumo model is studied in the framework of analytic theory of differential equations. The Nevanlinna theory is used to find all meromorphic solutions of a second-order ordinary differential equation related to the FitzHugh-Nagumo model. As a consequence new exact solutions of the FitzHugh-Nagumo system are obtained in explicit form.