Weakly Nonlinear Theory of Pattern-Forming Systems with Spontaneously Broken Isotropy

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Abstract
Quasi-two-dimensional pattern-forming systems with spontaneously broken isotropy represent a novel symmetry class, that is, experimentally accessible in electroconvection of homeotropically aligned liquid crystals. We present a weakly nonlinear analysis leading to amplitude equations which couple the short-wavelength patterning mode with the Goldstone mode resulting from the broken isotropy. The new coefficients in these equations are calculated from the hydrodynamics. Simulations exhibit a new type of spatiotemporal chaos at onset. The results are compared with experiments.
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