Soliton hierarchies associated with Lie algebra sp(6)

TL;DR

This paper constructs two classes of integrable soliton hierarchies linked to the symplectic Lie algebra sp(6), derives their Hamiltonian structures, and develops an integrable coupling system using the Kronecker product.

Contribution

It introduces new soliton hierarchies associated with sp(6), derives their Hamiltonian structures, and constructs an integrable coupling system, expanding the understanding of symplectic Lie algebra applications.

Findings

Two classes of integrable soliton hierarchies constructed.

Hamiltonian structures derived via Tu scheme and trace identity.

An integrable coupling system developed using Kronecker product.

Abstract

In this paper, by selecting appropriate spectral matrices within the loop algebra of symplectic Lie algebra sp(6), we construct two distinct classes of integrable soliton hierarchies. Then, by employing the Tu scheme and trace identity, we derive the Hamiltonian structures of the aforementioned two classes of integrable systems. From these two classes of integrable soliton hierarchies, we select one particular hierarchy and employ the Kronecker product to construct an integrable coupling system.