A type of new integrable hierarchy and its expanding integrable system

A new isospectral problem is designed by considering a subalgebra of loop algebra , which possesses two power gaps of spectral parameter λ. It follows that a new type of integrable system is obtained by choosing suitable modified term and Tu-model, which has bi-Hamiltonian structure. Furthermore, constructing a new five-dimensional loop algebra gives rise to a kind of expanding integrable system of the obtained system.