Transverse Front Instability in Bistable Systems with Long-Range Interactions

Using the Ginzburg-Landau equation with a long-range interaction, we study the stability of a planar front with respect to transverse perturbations in bistable systems. It is well known that when a bistable system has competiting short-range and long-range interactions, the front connecting two stable states can exhibit transverse instability. We focus on the effects of the nonlocal nature of the interaction, using long-range interactions with exponential decay (weak nonlocality) and power-law decay (strong nonlocality). It is found that in the former case, the planar front can be stabilized by varying a parameter value, while in the latter case, the strong nonlocal nature of the interaction prevents stabilization of the front.