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Title of Journal: Acta Appl Math

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Abbravation: Acta Applicandae Mathematicae

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Springer Netherlands

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DOI

10.1007/bf00433462

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1572-9036

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Virasoro Action on PseudoDifferential Symbols and

Authors: Partha Guha
Publish Date: 2008/10/21
Volume: 108, Issue: 2, Pages: 215-234
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Abstract

Using Grozman’s formalism of invariant differential operators we demonstrate the derivation of N=2 CamassaHolm equation from the action of VectS 12 on the space of pseudodifferential symbols We also use generalized logarithmic 2cocycles to derive N=2 super KdV equations We show this method is equally effective to derive CamassaHolm family of equations and these system of equations can also be interpreted as geodesic flows on the BottVirasoro group with respect to right invariant H 1metric In the second half of the paper we focus on the derivations of the fermionic extension of a new peakon type systems This new oneparameter family of N=1 super peakon type equations known as N=1 super bfield equations are derived from the action of VectS 11 on tensor densities of arbitrary weights Finally using the formal Moyal deformed action of VectS 11 on the space of Pseudodifferential symbols to derive the noncommutative analogues of N=1 super bfield equationsThis article is published under an open access license Please check the Copyright Information section for details of this license and what reuse is permitted If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and reuse information please contact the Rights and Permissions team

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