Meromorphic solutions in the Fitzhugh-Nagumo model
The system of Fitz-Nagumo differential equations \[ (1) \quad v_t=v-v^3 - u+\sigma, \quad \tau u_t=v-\beta u-\alpha, \quad \alpha , \beta, \sigma, \tau \in C \] is considered in the paper. For this system the authors presented two new transcendental solutions. These solutions are obtained as a result of the description of all meromorphic solutions of the auxiliary equation \[ 2\tau ww_{tt}-\tau w_t^2+2\{3 \tau w^2+(\beta-\tau )w\}w_t+4\beta w^3+4(1-\beta)w^2=0 \] associated with the system (1) for certain values of parameters.
scientific article; zbMATH DE number 6891851
scientific article