Two-dimensional supersymmetric nonlinear equations associated with embeddings of the subsuperalgebra $\mathrm{osp}(1,2)$ in lie superalgebras

The paper gives the construction of a large class of two-dimensional supersymmetric nonlinear systems that are associated through a Lax type representation with the local part of an arbitrary Lie superalgebra $\mathfrak G$ with Grassmann structure. The grading of $\mathfrak G$ is realized by the Cartan element of its subsuperalgebra $\mathrm{osp}(l, 2)$. Sufficient conditions are established for exact integrability of the obtained systems, the simplest special ease of which is the supersymmetric generalization of the two-dimensional Toda chain.