A note on the properties of a family of travelling-wave solutions arising in cubic autocatalysis

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Abstract
The propagating reaction–diffusion waves that may develop in the isothermal, autocatalytic system A+2B→3B, from a local initial input of the autocatalyst B, are considered. We find that travelling-wave solutions exist for all propagation speeds . It is shown that the travelling-wave solution with minimum propagation speed , exhibits exponential decay in the concentration of the autocatalyst B ahead of the wavefront, whilst, for faster travelling waves, with , the autocatalyst concentration decays only algebraically. This difference in behaviour between the minimum-speed and faster-speed waves has implications concerning the selection of the long-time wave speed when such travelling waves are generated from an initial-value problem