The Non-isospectral Integrable Hierarchies Associated with Lie Algebra $$\mathfrak {sp}(6)$$

In this paper, we consider non-isospectral problems of two distinct dimensions on the loop algebra of the symplectic Lie algebra $$\mathfrak {sp}(6)$$, and construct two integrable systems. Furthermore, we derive their Hamiltonian structures using the Tu scheme. Additionally, we construct an integrable hierarchy on the generalized Lie algebra $$\mathfrak {Gsp}(6)$$ and establish its Hamiltonian structure as well.