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

The conditions are derived for the onset of lateral instabilities in planar waves propagating in a chemical system based on cubic autocatalysis couple d with autocatalyst decay, represented by the parameter kappa. The results from a linear stability analysis of the corresponding traveling wave equati ons are presented and compared with predictions obtained from a "thin front " analysis. Instabilities arise when delta, the ratio of the diffusion coef ficients of the reactant and autocatalyst, is greater than some critical va lue delta (crit), with delta (crit) being found to depend strongly on kappa . Numerical simulations of the full initial-value problem are also determin ed and confirm the theoretical predictions. (C) 2001 American Institute of Physics.