Lateral instabilities in cubic autocatalytic reaction fronts: The effect of autocatalyst decay

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The conditions are derived for the onset of lateral instabilities in planar waves propagating in a chemical system based on cubic autocatalysis coupled with autocatalyst decay, represented by the parameter κ. The results from a linear stability analysis of the corresponding traveling wave equations are presented and compared with predictions obtained from a “thin front” analysis. Instabilities arise when δ, the ratio of the diffusion coefficients of the reactant and autocatalyst, is greater than some critical value δcrit, with δcrit being found to depend strongly on κ. Numerical simulations of the full initial-value problem are also determined and confirm the theoretical predictions.