Penta-Hepta Defect Motion in Hexagonal Patterns

The structure and dynamics of penta-hepta defects (PHD's) in hexagonal patterns are studied in the framework of coupled amplitude equations for the underlying plane waves. An analytical solution for the phase field of moving PHD is found in the far field, which generalizes the static solution due to Pismen and Nepomnyashchy. The mobility tensor of the PHD is calculated using a combined analytical and numerical approach. The results for the velocity of a PHD climbing in slightly nonoptimal hexagonal patterns are compared with numerical simulations of amplitude equations. The interaction of penta-hepta defects in optimal hexagonal patterns is considered.