Action potential solitons and waves in axons

We show that the action potential signals generated by the Hodgkin-Huxley cable model are reaction-diffusion solitons and waves. Action potential spikes travelling in opposite directions of the axon annihilate when colliding with each other or with the axon boundaries. Through numerical simulations, we characterise the properties of these action potentials, deriving their characteristic curves. We propose several tests to validate or falsify the Hodgkin-Huxley cable model.