CAUSTICS OF NONLINEAR-WAVES AND RELATED QUESTIONS

Patterns of parallel and equidistant layers are rather common in physical systems, as smectic liquid crystals or Rayleigh-Benard rolls in thermal convection. Although a minimization principle would impose perfectly straight layers, boundary conditions may change this when they impose the layers to be parallel to a closed smooth curve. Then a Huygens-like construction allows to draw the full pattern and yields caustics in general for linear wave equations. I show that, in nonlinear systems, those caustics are to be replaced by grain boundaries, and cusps by end of those grain boundaries. I study to the equivalent of the diffraction dressing of those grain boundaries by using a phase equation approach. © 1990 IOP Publishing Ltd.