Formation of planar static patterns using separated gaps of wave numbers in a generalized Swift-Hohenberg model

Mechanisms for pattern formation in biological organisms and chemical reactions have been broadly studied in last half of past century. Pattern formation also is frequently observed in many experiments. Traditional static patterns on the plane are patches forming hexagons, stripes and inverted hexagonal patches. Frequently, they are studied using reaction-diffusion models. The equation of Swift-Hohenberg also has been a paradigm for the formation of these structures, but also for studies of localized patterns. In this paper, we continue the analysis of behavior about a generalized Swift-Hohenberg equation considered previously. Setting a positive distance between two gaps of wave numbers, new patterns having different shapes and sizes can be produced with the proposed model.