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Theory of light-matter interaction in nematic liquid crystals and the second Painlevé equation

  • Marcel G. Clerc
  • Juan Diego Dávila
  • Michał Kowalczyk
  • Panayotis Smyrnelis
  • Estefania Vidal-Henriquez
Article

Abstract

We study global minimizers of an energy functional arising as a thin sample limit in the theory of light-matter interaction in nematic liquid crystals. We show that depending on the parameters various defects are predicted by the model. In particular we show existence of a new type of topological defect which we call the shadow kink. Its local profile is described by the generalized Hastings and McLeod solutions of the second Painlevé equation (Claeys et al. in Ann Math 168(2):601–641, 2008; Hastings and McLeod in Arch Ration Mech Anal 73(1):31–51, 1980). As part of our analysis we give a new proof of existence of these solutions.

Mathematics Subject Classification

35J20 35J61 35Q56 35Q60 

Notes

Acknowledgements

We would like to thank William Troy and Stuart Hastings for observations that helped us to implement some important improvements in the present version of this work. We would like to thank also Peter Clarkson for bringing reference [15] to our attention.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Marcel G. Clerc
    • 1
  • Juan Diego Dávila
    • 2
  • Michał Kowalczyk
    • 2
  • Panayotis Smyrnelis
    • 3
  • Estefania Vidal-Henriquez
    • 4
  1. 1.Departamento de Física, FCFMUniversidad de ChileSantiagoChile
  2. 2.Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (UMI 2807 CNRS)Universidad de ChileSantiagoChile
  3. 3.Centro de Modelamiento Matemático (UMI 2807 CNRS)Universidad de ChileSantiagoChile
  4. 4.Max Planck Institute for Dynamics and Self-OrganizationGöttingenGermany

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