Zigzag and varicose instabilities of a localized stripe

A localized stripe solution to a reaction-diffusion equation can lose stability simultaneously to zigzag and varicose perturbations at a codimension-two point. The resulting mode interaction is described by O(2)xZ(2) equivariant amplitude equations. Stationary mixed-mode solutions are found which can undergo instabilities to breathing modes or to patterns which travel along the stripe.