Supersymmetric kuper camassa - Holm equation and geodesic flow: A novel approach

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We use the logarithmic 2-cocycle and the action of V ect (S1) on the space of pseudodifferential symbols to derive one particular type of supersymmetric KdV equation, known as Kuper-KdV equation. This equation was formulated by Kupershmidt and it is different from the Manin-Radul-Mathieu type equation. The two Super KdV equations behave differently under a supersymmetric transformation and Kupershmidt version does not preserve SUSY transformation. In this paper we study the second type of supersymmetric generalization of the Camassa-Holm equation correspoding to Kuper-KdV equation via standard embedding of super vector fields into the Lie algebra of graded pseudodifferential symbols. The natural lift of the action of superconformal group SDiff yields SDiff module. This method is particularly useful to construct Moyal quantized systems.

Original languageBritish English
Pages (from-to)1-16
Number of pages16
JournalInternational Journal of Geometric Methods in Modern Physics
Issue number1
StatePublished - Feb 2008


  • Area preserving
  • Noncommutative integrable systems
  • Pseudodifferential symbols
  • Super KdV
  • Supersymmetry


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