Doubly periodic and multiple pole solutions of the sinh-Poisson equation: Application of reciprocal transformations in subsonic gas dynamics

  • Authors:

  • K. W. Chow;C. C. Mak;C. Rogers;W. K. Schief

  • Affiliations:

  • Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong;Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong;Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems, University of New South Wales, Sydney, Australia;Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems, University of New South Wales, Sydney, Australia

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2006

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Abstract

Vortex patterns associated with the sinh-Poisson equation arise in a remarkable manner as relaxation states of the Navier-Stokes equations. Here, doubly periodic and multiple-pole solutions of the sinh-Poisson equation are generated via the Hirota bilinear operator formalism and exploitation of the phenomenon of coalescence of wave numbers. It is then shown how the multi-parameter reciprocal transformations of gas dynamics may be applied to a seed doubly periodic solution of the sinh-Poisson equation to generate associated periodic vortex structures valid in the subsonic flow of a generalized Karman-Tsien gas.