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arXiv · 2509.25995

Two new super integrable hierarchies and a generalized super-AKNS hierarchy

Yanhui Bi·Bo Yuan·Yuqi Ruan·Tao Zhang
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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.

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Yanhui Bi, Bo Yuan, Yuqi Ruan, Tao Zhang. 2025-09-30. Two new super integrable hierarchies and a generalized super-AKNS hierarchy. https://arxiv.org/abs/2509.25995

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