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)


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.


Riemann Surface Burger Equation Physical Region Viscosity Limit Riemann Sheet 
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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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