An integrable generalization of the super Kaup-Newell soliton hierarchy and its bi-Hamiltonian structure

An integrable generalization of the super Kaup-Newell(KN) isospectral problem is introduced and its corresponding generalized super KN soliton hierarchy are established based on a Lie super-algebra B(0,1) and super-trace identity in this paper. And the resulting super soliton hierarchy can be put into a super bi-Hamiltonian form. In addition, a generalized super KN soliton hierarchy with self-consistent sources is also presented.

💡 Research Summary

The paper presents a systematic construction of a generalized super‑Kaup‑Newell (KN) soliton hierarchy by exploiting the Lie super‑algebra B(0,1) and the super‑trace identity. Starting from the standard super‑KN isospectral problem, the authors introduce a nonlinear deformation parameter ω = μ(q r + 2αβ), where μ is an arbitrary even constant, q and r are even potentials, and α, β are odd potentials. When μ = 0 the deformation disappears and the usual super‑KN problem is recovered.

A spatial Lax operator M is defined with this deformation, and an auxiliary operator N is expanded as a formal series in the spectral parameter λ. By imposing the stationary zero‑curvature condition Nₓ =