Supersymmetry of the Schroedinger and Korteweg-de Vries operators

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dc.creatorLeites, Dimitry
dc.creatorPeiqi, Xuan
dc.date1997-10-06
dc.date.accessioned2026-07-07T04:23:42Z
dc.date.available2026-07-07T04:23:42Z
dc.descriptionIn 70's A.A. Kirillov interpreted the stationary Schroedinger (Sturm-Liouville) operator as an element of the dual space to the Virasoro algebra, i.e., the nontrivial central extension of the Witt algebra. He interpreted the KdV operator in terms of the stabilizer of the Schroedinger operator. By studying the coadjoint representation of the simplest nontrivial central extension of a simplest stringy superalgebra, the Neveu--Schwarz superalgebra, Kirillov connected solutions of the KdV and Schroedinger equations. We extend Kirillov's results and find all supersymmetric extension of the Schroedinger and Korteweg-de Vries operators associated with the 12 distinguished stringy superalgebras. We also take into account the odd parameters and the possibility for Time to be a $(1|1)$-dimensional supermanifold. The superization of construction due to Khesin e.a. (Drinfeld--Sokolov's reduction for the pseudodifferential operators) relates the complex powers of the Schroedinger operators we describe to the superized KdV-type hierarchies labeled by complex parameter. Our construction brings the KdV-type equations directly in the Lax form guaranteeing their complete integrability.
dc.descriptionLaTeX, 15 pages
dc.identifierhttps://arxiv.org/abs/hep-th/9710045
dc.identifierhttp://arxiv.org/abs/hep-th/9710045
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/55131
dc.subjectHigh Energy Physics - Theory
dc.titleSupersymmetry of the Schroedinger and Korteweg-de Vries operators
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