Caustics of Nonlinear Waves and Related Questions
Y. Pomeau; Y. Pomeau; Laboratoire de Physique Statistique - 24, rue Lhomond, 75231 Paris Cedex 05, France
Журнал:
EPL (Europhysics Letters)
Дата:
1990-04-15
Аннотация:
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 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 too the equivalent of the diffraction dressing of those grain boundaries by using a phase equation approach.
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