Two-dimensional supersymmetric nonlinear equations associated with embeddings of the subsuperalgebra osp(1,2) in Lie superalgebras
type: Item
instance of: scholarly article
title: Two-dimensional supersymmetric nonlinear equations associated with embeddings of the subsuperalgebra osp(1,2) in Lie superalgebras
zbMATH Open document ID: 0593.58045
DOI: 10.1007/BF01038555
author: A. N. Leznov
author: Mikhail V. Saveliev
published in: Theoretical and Mathematical Physics
publication date: 1984-01-01T00:00:00Z
review text: This paper continues the authors' earlier work on super-symmetric nonlinear equations [see, e.g., Commun. Math. Phys. 89, 59-75 (1983; Zbl 0536.35068) and references given therein]. The object of this study is some Lax type equation, which characterizes the embeddings of \((2+2)\) dimensional supermanifolds into some \({\mathbb{Z}}\)-graded Lie superalgebra \({\mathcal G}\). The aim is to investigate integrability conditions of this equation and to find explicit solutions. The present paper is concerned with the case where \({\mathcal G}\) contains osp(1,2) as sub-superalgebra and its \({\mathbb{Z}}\)-grading is realized by the Cartan element of osp(1,2). Sufficient conditions for exact integrability are given and some examples are mentioned (supersymmetric generalizations of the two-dimensional Toda chain, of the Liouville equation, and of the sine-Gordon equation).
Mathematics Subject Classification ID: 58J60
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 17A70
Mathematics Subject Classification ID: 81T60
zbMATH DE Number: 3953913
zbMATH Keywords: super-symmetric nonlinear equations
zbMATH Keywords: Lax type equation
zbMATH Keywords: two-dimensional Toda chain
zbMATH Keywords: Liouville equation
zbMATH Keywords: sine-Gordon equation
reviewed by: Volker Perlick
MaRDI profile type: Publication
cites work: Supersymmetric two-dimensional Toda lattice
full work available at URL: https://doi.org/10.1007/bf01038555
OpenAlex ID: W1972388669
description: scientific article; zbMATH DE number 3953913