Some Soliton Hierarchies Associated with Lie Algebras mathfrak {sp}(4) and mathfrak {so}(5)

Abstract

Based on the symplectic Lie algebra mathfrak {sp}(4), we obtain two integrable hierarchies of mathfrak {sp}(4), and by using the trace identity, we give their Hamiltonian structures. Then, we use 2times 2 Kronecker product, and construct integrable coupling systems of one soliton equation. Next, we consider two bases of Lie algebra mathfrak {so}(5), and we get the corresponding two integrable hierarchies. Finally, we discuss the relation between the integrable hierarchies of two different bases associated with Lie algebra mathfrak {so}(5).