Two-dimensional supersymmetric nonlinear equations associated with embeddings of the subsuperalgebra osp(1,2) in Lie superalgebras
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).
scientific article; zbMATH DE number 3953913