Caustics of Nonlinear Waves and Related Questions

Abstract

Patterns of parallel and equidistant layers are rather common in physical systems, as smectic liquid crystals or Rayleigh-Bénard rolls in thermal convection. Although a minimisation 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 ends of those grain boundaries. I study too the equivalent of the diffraction dressing of those grain boundaries by using a phase equation approach.