Open AccessSUPERSYMMETRIC KUPER CAMASSA–HOLM EQUATION AND GEODESIC FLOW: A NOVEL APPROACH
Author(s) -
Partha Guha
Publication year - 2008
Publication title -
international journal of geometric methods in modern physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.414
H-Index - 39
eISSN - 1793-6977
pISSN - 0219-8878
DOI - 10.1142/s0219887808002618
Subject(s) - mathematics , korteweg–de vries equation , supersymmetry , transformation (genetics) , pure mathematics , generalization , type (biology) , action (physics) , mathematical physics , algebra over a field , mathematical analysis , physics , quantum mechanics , ecology , biochemistry , chemistry , nonlinear system , biology , gene
We use the logarithmic 2-cocycle and the action of V ect(S,) 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 Kuper- shmidt 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 cor- respoding 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. Mathematical Classification 17B68, 37K10, 58J40. 1 Keywords and Keyphrases : supersymmetry, pseudodifferential symbols, su-
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