Search

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
88/2007

Supersymmetric Kuper Camassa-Holm Equation and Geodesic Flow : A Novel Approach

Partha Guha

Abstract

We use the logarithmic $2$-cocycle and the action of $Vect(S^1)$ 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.

Received:
13.09.07
Published:
13.09.07
MSC Codes:
17B6, 37K10, 58J40
Keywords:
supersymmetry, pseudodifferential symbols, super KdV

Related publications

inJournal
2008 Repository Open Access
Partha Guha

Supersymmetric Kuper Camassa-Holm equation and geodesic flow : a novel approach

In: International journal of geometric methods in modern physics, 5 (2008) 1, pp. 1-16