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Complex Singularities and the Riemann Surface for the Burgers Equation

  • D. Bessis
  • J. D. Fournier
Part of the Research Reports in Physics book series (RESREPORTS)

Abstract

The analytic structure of the solution of the Burgers equations is analysed: the viscous solution has an infinite number of complex poles. When the viscosity tends to zero, these poles condense, producing the inviscid singularities. A Riemann surface is attached to those non polar singularities. As a consequence, a shock appears to be the permutation of two Riemann sheets. This phenomenon can also be understood as a phase transition in a Curie-Weiss model.

Keywords

Riemann Surface Burger Equation Physical Region Viscosity Limit Riemann Sheet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin, Heidelberg 1990

Authors and Affiliations

  • D. Bessis
    • 1
  • J. D. Fournier
    • 2
  1. 1.Service de Physique Théorique de SaclayLaboratoire de l’Institut de Recherche Fondamentale du Commissariat à l’Energie AtomiqueGif-sur-Yvette CedexFrance
  2. 2.ObservatoireMont-GrosNice CedexFrance

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