Novel soliton hierarchies of Levi type and their bi-Hamiltonian structures

We present two new matrix spectral problems, and construct the corresponding soliton hierarchies of Levi type with the aid of symbolic computation by Maple. Bi-Hamiltonian structures of the resulting soliton hierarchies are obtained by means of the trace identity. Thus it is shown that these soliton hierarchies are Liouville integrable.

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