The nonisospectral integrable hierarchies associated with Lie algebra $\mathfrak{s}\mathfrak{p}(6)$

In this paper, we consider nonisospectral problems of two distinct dimensions on the loop algebra of the symplectic Lie algebra $\mathfrak{s}\mathfrak{p}(6)$, 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 $\mathfrak{G}\mathfrak{s}\mathfrak{p}(6)$ and establish its Hamiltonian structure as well.