The quasi-AKNS and quasi- so(3) type AKNS hierarchies as well as a gallery of simple Lie algebras contained in sl(3 ; ℂ)

Abstract

Abstract This paper provides a new representation of s l ( 3 ; ℂ ) , i.e., a high-dimensional special linear Lie algebra A , which contributes to the generation of a series of simple Lie algebras owning different bases with inequable commutators. Their counterparts are obtained in succession by using some special invertible linear transformations. As applications, the quasi-AKNS and quasi- s o ( 3 ) type AKNS Hamiltonian hierarchies as well as their nonlinear continuous integrable couplings with the Hamiltonian structures are established, respectively.