Virasoro action on pseudo-differential symbols and (noncommutative) supersymmetric peakon type integrable systems
type: Item
instance of: scholarly article
title: Virasoro action on pseudo-differential symbols and (noncommutative) supersymmetric peakon type integrable systems
zbMATH Open document ID: 1220.37052
author: Partha Guha
published in: Acta Applicandae Mathematicae
publication date: 2009-11-16T00:00:00Z
review text: From the author's abstract: ``Using Grozman's formalism of invariant differential operators we demonstrate the derivation of the \(N=2\) Camassa-Holm equation from the action of \(\text{Vect}(S^{1|2})\) on the space of pseudo-differential symbols. We also use generalized logarithmic \(2\)-cocycles to derive \(N=2\) super KdV equations. We show this method is equally effective to derive Camassa-Holm family of equations and these system of equations can also be interpreted as geodesic flows on the Bott-Virasoro group with respect to right invariant \(H^{1}\)-metric. In the second half of the paper we focus on the derivations of the fermionic extension of a new peakon type systems. This new one-parameter family of \(N=1\) super peakon type equations, known as \(N=1\) super \(b\)-field equations, are derived from the action of \(\text{Vect}(S^{1|1})\) on tensor densities of arbitrary weights. Finally, using the formal Moyal deformed action of \(\text{Vect}(S^{1|1})\) on the space of pseudo-differential symbols to derive the noncommutative analogues of \(N=1\) super \(b\)-field equations.''
reviewed by: Luen-Chau Li
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 17B68
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 58J40
Mathematics Subject Classification ID: 37K30
zbMATH DE Number: 5633618
zbMATH Keywords: pseudo-differential symbols
zbMATH Keywords: super KdV
zbMATH Keywords: Camassa-Holm equation
zbMATH Keywords: geodesic flow
zbMATH Keywords: super \(b\)-fields equations
zbMATH Keywords: Moyal deformation
zbMATH Keywords: non-commutative integrable systems
MaRDI profile type: Publication
full work available at URL: s10440-008-9310-7
OpenAlex ID: W2139609135
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DOI: 10.1007/S10440-008-9310-7
description: scientific article; zbMATH DE number 5633618