Dynamics of dislocations in hexagonal patterns

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Abstract
The dynamics and interaction of dislocations of roll systems forming hexagonal patterns is studied numerically within a model of three resonantly coupled Newell-Whitehead-Segel equations. It is shown that an individual dislocation is driven away as a result of phase synchronization among roll patterns. Two dislocations with opposite topological charges belonging to different roll systems are attracted to each other and form a ‘‘penta-hepta’’ defect on the background of the perfect hexagonal pattern, which is stable and motionless.