Pattern selection and low-dimensional chaos in the driven damped two-dimensional sine-Gordon equation

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Abstract
It is shown numerically that the long-time behaviour of a two-dimensional homogeneously driven and damped sine-Gordon equation with periodic boundary conditions exhibits striking spatio-temporal coupling, resulting in the spatial pattern selection, low dimensional chaos, and coexisting coherence and chaos. Attractors with spontaneously generated high spatial symmetry include uniformly 'running' states, and pattern conversion from two dimensions to one. Synergetic comparisons with equilibrium Hamiltonian systems with competing interactions are suggested.