The effect of a finite geometry on the two-dimensional complex Ginzburg-Landau equation is addressed. Boundary effects induce the formation of novel states. For example, target-like solutions appear as robust solutions under Dirichlet boundary conditions. Synchronization of plane waves emitted by boundaries, entrainment by corner emission, and anchoring of defects by shock lines are also reported.

Citing articles:

1. Boundary effects in extended dynamical systems,

V.M. Eguiluz et al, Physica A 283, 48-51 (2000).
2. Spatiotemporal chaos, localized structures and synchronization in the vector complex Ginzburg-Landau equation
   E. Hernandez-Garcia et al, Int. J. Bifurcation Chaos 9, 2257-2264 (1999).

The Complex Ginzburg-Landau Equation in the Presence of Walls and Corners

¹Center for Chaos and Turbulence Studies (CATS), The Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark
²Instituto Mediterráneo de Estudios Avanzados (IMEDEA) CSIC-UIB, E-07071 Palma de Mallorca, Spain

We investigate the influence of walls and corners (with Dirichlet and Neumann boundary conditions) in the evolution of twodimensional autooscillating fields described by the complex Ginzburg-Landau equation. Analytical solutions are found, and arguments provided, to show that Dirichlet walls introduce strong selection mechanisms for the wave pattern. Corners between walls provide additional synchronization mechanisms and associated selection criteria. The numerical results fit well with the theoretical predictions in the parameter range studied.

PACS: 05.45.-a, 47.54.+r