A new super integrable hierarchy and a generalized super-AKNS hierarchy

Abstract: In this paper, we investigate a non-isospectral problem on the loop algebra of the Lie superalgebra osp(1,6), and construct an super integrable system using the supertrace identity. The resulting super integrable system can be reduced to the super-AKNS hierarchy under certain conditions. By reconsidering a new (2 + 1)-dimensional non-isospectral problem with spectral matrices satisfying these conditions, we obtain a (2+1)-dimensional generalization of the superAKNS hierarchy.