An investigation was made of the statics, nucleation, and dynamics of such pairs in a 1-dimensional, 1-component reaction-diffusion equation with a piece-wise linear non-linearity. The stabilization of the kink-antikink pairs was attributed to the presence of a strongly non-local inhibitor. A saddle-node bifurcation of a metastable kink-antikink pair was found, with a separation that was proportional to ln[L], where L was the length of the sample. The kink-antikink pairs became globally stable at a characteristic separation that was proportional to L. The nucleation of a kink-antikink pair from the metastable uniform state differed from the case without non-locality; due mainly to a change in the activation energy that was induced by the non-locality. An investigation was also made of the dynamics of the stable kink-antikink pair in the presence of an external driving force and a lowered density of point-like impurities. In particular, expressions were derived for the mobility and average elongation of the kink-antikink pairs.

T.Christen: Zeitschrift für Naturforschung, 1995, 50a[12], 1128-34