EXISTENCE OF SOLITARY TRAVELING WAVE SOLUTIONS OF A MODEL OF THE BELOUSOV-ZHABOTINSKII REACTION

A system of partial differential equations which model the reaction-diffusion dynamics of the Belousov-Zhabotinskii chemical reaction is investigated. Over a physically reasonable range of parameters for which the system exhibits no temporal oscillations, it is shown that the equations have a solitary traveling wave solution. These waves appear to correspond to the ″trigger waves″ observed experimentally in the reaction. In addition, it is shown that if the autocatalytic reaction is sufficiently slow, then as expected from the chemistry, the model has no solitary traveling wave solutions. The wave speed is numerically computed and shown to be close to the observed speed of the trigger waves. Also, the dependence of the wave speed on the various measurable physical parameters in the model is computed and shown to be in excellent agreement with that observed.