Integrable counterparts of the D-Kaup-Newell soliton hierarchy

Two integrable counterparts of the D-Kaup–Newell soliton hierarchy are constructed from a matrix spectral problem associated with the three dimensional special orthogonal Lie algebra soð3;RÞ. An application of the trace identity presents Hamiltonian or quasiHamiltonian structures of the resulting counterpart soliton hierarchies, thereby showing their Liouville integrability, i.e., the existence of infinitely many commuting symmetries and conserved densities. The involved Hamiltonian and quasi-Hamiltonian properties are shown by computer algebra systems. 2014 Elsevier Inc. All rights reserved.