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The Existence of Solitary Traveling Wave Solutions of a Model of the Belousov-Zhabotinskii Reaction

Richard J. Field and William C. Troy
SIAM Journal on Applied Mathematics
Vol. 37, No. 3 (Dec., 1979), pp. 561-587
Stable URL: http://www.jstor.org/stable/2100912
Page Count: 27
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The Existence of Solitary Traveling Wave Solutions of a Model of the Belousov-Zhabotinskii Reaction
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Abstract

We investigate a system of partial differential equations which model the reaction-diffusion dynamics of the Belousov-Zhabotinskii chemical reaction. Our system is developed from the Oregonator model of Field and Noyes. Over a physically reasonable range of parameters for which the system exhibits no temporal oscillations, we show 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 we show that if the autocatalytic reaction is sufficiently slow, then as expected from the chemistry, the model has no solitary traveling wave solutions. We numerically compute the wave speed and it is 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.

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