Abstract
Based on ansatz functions technique, we construct many types of novel wave structures and multiple lumpsoliton solutions to the generalized Fitzhugh-Nagumo (gFN)-equation. In particular, we obtain entirely exciting lump, lump 1-kink, lump 2-kink, lump-periodic, manifold periodic-soliton, periodic cross-rational, kink crossrational (KCR) solutions, interaction of the multi-lump and periodic solutions as well as breather style of solitary wave solutions. Using a transformation of dependent variable, which contain a controlling parameter (can control the direction, wave height and angle of the traveling wave), we build generalized breathers, rogue wave, Akhmediev breather, homoclinic breather, Ma breather, Kuznetsov-Ma breather and their relating rogue waves, multiwave, M-shaped rational and some various interactions. We show the results of our solutions graphically in distinct dimensions by assigning different values to the parameters.(c) 2022 Elsevier Ltd. All rights reserved.