Two new super integrable hierarchies and a generalized super-AKNS hierarchy
Exactly Solvable and Integrable Systems
2026-05-28 v3 Rings and Algebras
Abstract
In this paper, we investigate two non-isospectral problems on the loop algebra of the Lie superalgebra osp(1,6), and construct two super-integrable systems and their super Hamiltonian structure 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 super-AKNS hierarchy.
Keywords
Cite
@article{arxiv.2509.25995,
title = {Two new super integrable hierarchies and a generalized super-AKNS hierarchy},
author = {Yanhui Bi and Bo Yuan and Yuqi Ruan and Tao Zhang},
journal= {arXiv preprint arXiv:2509.25995},
year = {2026}
}