Local stability theory of solitary pulses in an active medium

Abstract

If the spatio-temporal chaos of an extended active medium is driven by repulsive or attractive interaction among localized coherent structures such as kinks and pulses, its dynamics can often be described by a low-dimensional dynamical system. This welcomed reduction in the degrees of freedom only occurs when the localized structures remain stable during their mutual interaction. It is shown that the structures can be destroyed by two types of local disturbance—an expanding radiation packet and a localized disturbance which travels with the structure. These two instabilities and the bifurcations they induce select the proper coherent structure and specify the dynamics of the generalized Kuramoto-Sivashinsky (gKS) equation in an extended domain. The possibility of describing pulse-radiation interaction by “resonance poles” also suggests that a more general coherent structure theory can be developed.