Ultrafast Traveling Spike Autosolitons in Reaction-Diffusion Systems

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Abstract
We have discovered a fundamentally new type of traveling wave solutions in reaction-diffusion systems—a traveling spike autosoliton. Using the proposed asymptotic method and the results of the numerical simulations, we investigated the shape of this autosoliton and the dependence of its basic characteristics on the system's parameters for the Brusselator. We have found that this autosoliton may have very large amplitude and velocity, and that its shape is in detailed qualitative agreement with that of the traveling pulses observed in the nerve tissue and in certain chemical reactions.