Stable Kink-Antikink Pairs in Bistable Reaction-Diffusion Systems with Strong Nonlocalities

Abstract

Abstract We investigate the statics, nucleation, and dynamics of stable kink-antikink pairs (KAP) in a one-dimensional, one-component reaction-diffusion equation with a piecewise linear nonlinearity. The stabilization of the KAP is due to the presence of a strongly nonlocal inhibitor. We find a saddle-node bifurcation of a metastable KAP with a separation proportional to In L, where L is the length of the sample. The KAP becomes globally stable at a characteristic separation proportional to √L. The nucleation of a KAP from the metastable uniform state differs from the case without nonlocality mainly by a change of the activation energy induced by the nonlocality. Furthermore, we investigate the dynamics of the stable KAP in the presence of an external driving force and a diluted density of pointlike impurities; in particular, we derive expressions for the mobility and the average elongation of the KAP.