Nonlinear analysis of spatial structures in two-dimensional anisotropic pattern forming systems

Abstract

Motivated in particular by recent experiments on convective instabilities in nematic liquid crystals we examine the possible stationary patterns in anisotropic quasi-two-dimensional systems. The generalized SH-model we use exhibits the typical Lifshitz point, which separates the regions of normal and of oblique rolls at threshold. Above threshold the two-dimensional wavenumber regions of stable roll solutions take on interesting shapes in the vicinity of the Lifshitz point. Undulated (wavy) rolls also exist metastably in a narrow parameter range. We derive envelope equations which show that this scenario is general near threshold. Our results suggest experimental investigation, especially in the neighborhood of the Lifshitz point.