Abstract
We show the existence of travelling wave solutions to a generalized system of nerve equations which include the case where the slow variable also has a diffusion effect. We are mainly interested in the persistency of the pulse solution of the Fitz Hugh-Nagumo equations. Using an isolating block and a contracting block family, an intuitive idea derived from the shooting method becomes mathematically rigorous.
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Ogawa, T. Travelling wave solutions to a generalized system of nerve equations. Japan J. Appl. Math. 7, 255–276 (1990). https://doi.org/10.1007/BF03167844
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DOI: https://doi.org/10.1007/BF03167844