A New Liouville Integrable Hierarchy and Its Bi-Hamiltonian Structure

It is important to search for new integrable equations hierarchies in soliton theory.First,a new equations hierarchy was constructed.Taking use of higher-dimension Lie algebra A2 and the corresponding loop algebra 2,it was proved that the equations hierarchy is Lax integrable.Then,the bi-Hamiltonian structures of the Lax integrable hierarchy were constructed by making use of the trace identity.Finally,the infinitely conserved densities for the equations hierarchy was obtained and it was proved that the Lax equations hierarchy is Liouville integrable.