A new integrable hierarchy and constrained flows, its expanding integrable system

A new subalgebra of loop algebra A∼2 is first constructed. It follows that an isospectral problem is established. Using Tu-pattern gives rise to a new integrable hierarchy, which possesses bi-Hamiltonian structure. Furthermore, by making use of bi-symmetry constraints, the generalized Hamiltonian regular representations for the hierarchy are obtained. Finally, we obtain an expanding integrable system of this hierarchy by applying a scalar transformation between two isospectral problems and constructing a five-dimensional loop algebra G∼.