New Soliton Hierarchies Associated with the Lie Algebra so(3, ℝ) and their BI-Hamiltonian Structures

We present three new matrix spectral problems, based on the real special orthogonal Lie algebra so (3, ℝ), and construct the corresponding asymmetric soliton hierarchies of AKNS type, KN type and WKI type with the aid of symbolic computation by Maple. Bi-Hamiltonian structures yielding Liouville integrability of the resulting soliton hierarchies are furnished by the trace identity, and so, all newly presented equations possess infinitely many commuting symmetries and conservation laws.