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

TL;DR

This paper develops nonisospectral integrable hierarchies related to the symplectic Lie algebra sp(6), constructing systems and their Hamiltonian structures, expanding understanding of integrable systems associated with Lie algebras.

Contribution

It introduces new nonisospectral integrable hierarchies linked to sp(6) and derives their Hamiltonian structures, extending previous work on integrable systems and Lie algebras.

Findings

Constructed two integrable systems from nonisospectral problems on sp(6)

Derived Hamiltonian structures for these systems using the Tu scheme

Established an integrable hierarchy on the generalized Lie algebra Gsp(6)

Abstract

In this paper, we consider nonisospectral 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.