Exact Solutions of Two-Dimensional Vortex Systems in Statistical Equilibrium

  • H. H. Chen
  • A. C. Ting
  • Y. C. Lee
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 30)


Statistical equilibrium states of two-dimensional vortex systems [1] are described by the solutions of a nonlinear elliptic partial differential equation, the sinh-Poisson equation ∇2 ø + λ2 sinh = ø, with (ø = 0 on a rectangular boundary. We present here the first general analytic solutions to such a nonlinear boundary value problem. Some of these solutions were obtained previously only through numerical means. Explicit solutions showing nonlinear superposition are displayed.


Imaginary Axis Elliptic Partial Differential Equation Statistical Equilibrium State General Analytic Solution Mirror Image Position 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • H. H. Chen
    • 1
  • A. C. Ting
    • 1
  • Y. C. Lee
    • 1
  1. 1.Laboratory for Plasma and Fusion Energy StudiesUniversity of MarylandCollege ParkUSA

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