Supersymmetric Kuper Camassa-Holm Equation and Geodesic Flow : A Novel Approach
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Submission date: 13. Sep. 2007
published in: International journal of geometric methods in modern physics, 5 (2008) 1, p. 1-16
DOI number (of the published article): 10.1142/S0219887808002618
MSC-Numbers: 17B6, 37K10, 58J40
Keywords and phrases: supersymmetry, pseudodifferential symbols, super KdV
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We use the logarithmic 2-cocycle and the action of on the space of Pseudo-differential 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 peudodifferential symbols. The natural lift of the action of superconformal group SDiff yields SDiff module. This method is particularly useful to construct Moyal quantized systems.