Caustics of Nonlinear Waves and Related Questions

  • Yves Pomeau
Part of the NATO ASI Series book series (NSSB, volume 225)


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.


Helmholtz Equation Geometrical Optic Roll Orientation Linear Wave Equation Smectic Liquid Crystal 


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Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • Yves Pomeau
    • 1
  1. 1.Laboratoire de Physique StatistiqueParis Cedex 05France

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